Bibliography: Set Theory with a Universal Set

Introduction

This is a comprehensive bibliography on axiomatic set theories which have a universal set. (Zermelo-Fraenkel set theory, the most widely studied set theory, does not have a universal set.) This field presently includes three main areas of study: "New Foundations", a set theory devised by W. van Orman Quine, the positive set theory of Helen Skala, and model-based extensions of Zermelo-Fraenkel set theory, initiated by Alonzo Church. Recent papers by Holmes (and the original papers of Andrzej Kisielwicz) on "double extension set theory" are referenced in the main body of the bibliography but not under "recent work"; the jury is still out on this system (two versions of which have been shown to be inconsistent) but if the surviving version is consistent, it must be admitted that it is a set theory with universal set.

For those unfamiliar with the field, two places to start are the New Foundations Home Page and Thomas Forster's book Set Theory with a Universal Set. A new option is afforded by the recent appearance of Holmes's elementary text.

Comments, corrections, and information about new publications should be sent to Randall Holmes. Announcements about both print and eprint publications are welcome.

Many thanks to Randall Holmes and Boise State University for hosting this web page, and to Thomas Forster, who provided the data for the first edition of this bibliography.

Last revision: March 2005 (and I don't always remember to update this date when I change it).

Recent Work

I have just finished upgrading the bibliography in March 2005: if anyone misses a reference to some of their stuff, please tell me and I will attend to it promptly (contrary to my practice of the last few years).

Where I have inserted notes, they refer to the item just above.

I am doing a further update (mostly involving work on positive set theory by Belgians) November 2005. Much of this is outdated (i.e., I have been tardy) and so will appear in the main part under the author's name rather than in the Recent Work section (unless it is very recent). But some of it does appear below: usually I put this stuff into recent work if it is dated 2003 or later (not all the way back to 1995)

I am in the process of updating in March 2008; this would be a good time to bring errors or omissions to my attention!

• Holmes, M. Randall[2008]
  Symmetry as a criterion for comprehension motivating Quine's ``New Foundations''
  Studia Logica, vol. 88, no. 2 (March 2008).
• Enayat, A.[2006]
  From Bounded Arithmetic to Second Order Arithmetic via Automorphisms
  Logic in Tehran, pp. 87--113, Lect. Notes Logic, 26, Assoc. Symbol. Logic, La Jolla, CA
  Note:the author says "includes the core results about automorphisms relevant to NFU + "the universe is finite". The results about NFU are announced in section 5.1 (but see also the introduction)."
• Libert, T.[2006 -- I believe this means "yet to appear"]
  More studies on the axiom of comprehension
  Cahiers du Centre de Logique, no. 15, Academia-Bruylant, Louvain-la-Neuve (Belgium).
• Hinnion, R.[2006]
  Intensional positive set theory
  Reports on Mathematical Logic, vol. 40.
• O. Esser and T. Libert[2005]
  On topological set theory
  Mathematical Logic Quarterly, vol. 51, pp. 263-273.
• Libert, T.[2005]
  Models for a Paraconsistent Set Theory
  Journal of Applied Logic, vol. 3, pp. 15-41.
• Esser, Olivier [2004]
  Une theorie positive des ensembles.
  Cahiers du Centre de Logique, vol. 13, Academia-Bruylant, Louvain-la-Neuve (Belgium), ISBN 2-8729-687-6.
• Libert, T.[2004]
  Semantics for naive set theory in many-valued logics, technique and historical account
  in, J. van Benthem and G. Heintzmann, eds., The age of alternative logics, Kluwer, 2004.
• Crabbé,M. [2004]
  Cuts and Gluts.
  To appear in the Journal of Applied Non-Classical Logics. Still downloadable at www.lofs.ucl.ac.be/log/perso/Crabbe/textes/
• Crabbé,M. [2004] L'égalité et l'extensionnalité.
  To appear in Logique et Analyse. Still downloadable at www.lofs.ucl.ac.be/log/perso/Crabbe/textes/
• Crabbé,M. [2004] Une élimination des coupures ne tolérant pas l'extensionnalité.
  To appear in Logique et Analyse. Still downloadable at www.lofs.ucl.ac.be/log/perso/Crabbe/textes/
  Note:Marcel says "Though not yet published, the [above] are connected with stratification and positive stuff"
• Enayat, Ali[2004]
  Automorphisms, Mahlo Cardinals, and NFU
  in Nonstandard Models of Arithmetic and Set Theory, (Enayat, A. and Kossak, R., eds.), Contemporary Mathematics, vol. 361, American Mathematical Society. Also available here.
• Forster, T. E.[2004]
  AC fails in the natural analogues of L and the cumulative hierarchy that model the stratified fragment of ZF.
  in Nonstandard Models of Arithmetic and Set Theory, (Enayat, A. and Kossak, R., eds.), Contemporary Mathematics, vol. 361, American Mathematical Society. There is a link from Forster's home page as well.
• Hinnion, R.[2003]
  About the coexistence of classical sets with non-classical ones: a survey
  Logic and Logical Philosophy, vol. 11, pp. 79-90.
• Holmes, M. R.[2002]
  Forcing in NFU and NF
  in M. Crabbe, C. Michaux, and F. Point, eds., A tribute to Maurice Boffa, Belgian Mathematical Society, 2002.
• Forster, T. E.[2001]
  Church-Oswald models for Set Theory
  in: Logic, Meaning and Computation: essays in memory of Alonzo Church, Synthese library 305, Kluwer, Dordrecht, Boston and London 2001.
• Forster, T. E.[2001]
  Games played on an illfounded membership relation.
  in A Tribute to Maurice Boffa ed Crabb\'e, Point, and Michaux. (Supplement to the December 2001 number of the Bulletin of the Belgian Mathematical Society)
• Forster, T. E.[2001]
  Translation of Specker, E.P. Dualit\"at (Dialektika, 12, pp 451--465; 1957) with a commentary
  in Follesdal, ed: Philosophy of Quine, 4, Logic, Modality and Philosophy of Mathematics pp 7-16. Taylor-and-Francis 2001.

  available on www.dpmms.cam.ac.uk/~tf/duality.ps

• Holmes, M. R.[2001]
  Foundations of mathematics in polymorphic type theory.
  Topoi, vol. 20, pp. 29-52.
  NOTE: this is my official answer to the claim by certain parties on the FOM list that mathematics must be defined in terms of what we can do in ZFC...
• Holmes, M. R.[2001]
  Strong axioms of infinity in NFU.
  Journal of Symbolic Logic, vol. 66, no. 1, pp. 87-116.
  (brief notice of errata with corrections to appear in a future issue).
• Holmes, M. R. and Alves-Foss, J.[2001]
  The Watson theorem prover.
  Journal of Automated Reasoning, vol. 26, no. 4, pp. 357-408.
• Holmes, M. R.[1999]
  Subsystems of Quine's ``New Foundations'' with Predicativity Restrictions.
  Notre Dame Journal of Formal Logic, vol. 40, no. 2, pp. 183-196.
  appeared physically in 2001.
• Crabbé,M. [2000]
  The rise and fall of typed sentences
  Journal of Symbolic Logic, vol. 65, no. 4, pp. 1858-1862.
• Crabbé,M. [2000]
  On the set of atoms.
  Logic Journal of the IGPL, Vol. 8, no. 6, pp. 751-759.
  Can be downloaded at: http://www3.oup.co.uk/igpl/Volume_08/Issue_06/#Crabbe
• Holmes, M. R.[2000]
  A strong and mechanizable grand logic
  in Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, Lecture Notes in Computer Science, vol. 1869, Springer-Verlag, pp. 283-300.
  This is the theoretical paper on the foundations of the Watson theorem prover.
• Boffa, Maurice[1999]
  On Specker's refutation of the axiom of choice.
  Abstract of a talk at a symposium in honor of Engeler and Specker, available from the author
  to appear in Logique et Analyse, 1999 issue (complete publication data to be added when available). Here is the abstract itself (PostScript). Also the abstract itself (PDF).
• Oksanen, M.[1999]
  The Russell-Kaplan Paradox and Other Modal Paradoxes: A New Solution
  Nordic Journal of Philosophical Logic, Vol. 4, No. 1, pp. 73-93, June 1999, Scandinavian University Press.
  Also available on- line at http://www.hf.uio.no/filosofi/njpl/
• Crabbé, M. [1999]
  L'axiome de l'infini dans NFU.
  C. R. Acad. Sci. Paris, t. 329, Série I, p. 1033-1035, 1999.
• Esser, Olivier [1999]
  On the consistency of a positive theory.
  Mathematical Logic Quarterly, vol. 45, no. 1, pp. 105-116.
• Holmes, M. R. [1998]
  Elementary set theory with a universal set.
  volume 10 of the Cahiers du Centre de logique, Academia, Louvain-la-Neuve (Belgium), 241 pages, ISBN 2-87209-488-1. See here for an on-line errata slip. By permission of the publishers, a corrected text is published online here; an official second edition will appear online eventually.
• Gian Aldo Antonelli[1998]
  Extensional Quotients for Type Theory and the Consistency Problem for NF.
  Journal of Symbolic Logic, vol. 63, n. 1, pp. 247-61, 1998.
• Dzierzgowski, Daniel[1998]
  Finite sets and natural numbers in intuitionistic TT without extensionality.
  Studia Logica, vol. 61, no. 3 (November 1998), pp. 417-428.
• Solovay, Robert[199?]
  The consistency strength of NFUB.
  preprint, available through logic e-prints on the WWW.
• Forster, Thomas [1997]
  Quine's NF, 60 years on.
  American Mathematical Monthly, vol. 104, no. 9 (November), pp. 838-845.
• Körner, F. [1998]
  Automorphisms moving all non-algebraic points and an application to N\ F.
  Journal of Symbolic Logic 63, p. 815-830.
• Dzierzgowski, Daniel[1996]
  Finite sets and natural numbers in intuitionistic TT, Notre Dame Journal of Formal Logic.
  vol. 37, no. 4 (1996), pp. 585-601.
• Esser, O. [1996]
  Inconsistency of GPK + AFA.
  Mathematical Logic Quarterly 42, pp. 104-108.
• Dziergowski, D. [1995]
  Models of intuitionistic TT and NF.
  Journal of Symbolic Logic 60, pp. 640-653.
• Holmes, M.R. [1995a]
  The equivalence of NF-style set theories with "tangled" type theories; the construction of omega-models of predicative NF (and more).
  Journal of Symbolic Logic 60, pp. 178-189.
• Holmes, M.R. [1995b]
  Untyped lambda-calculus with relative typing.
  Typed Lambda-Calculi and Applications (Proceedings of TLCA '95), Springer, pp. 235-248.
• Jech, T. [1995]
  OTTER experiments in a system of combinatory logic
  Journal of Automated Reasoning, 14, pp. 413-426.

Comprehensive Bibliography

• Aczel, Peter[1988]
  Non-Well-Founded Sets
  CSLI
  Note: the connections of this material to NF studies are somewhat tangential: the reasons for interest in non-well-foundedness are different in the two areas.But there are some connections.
• Gian Aldo Antonelli[1998]
  Extensional Quotients for Type Theory and the Consistency Problem for NF.
  Journal of Symbolic Logic, vol. 63, n. 1, pp. 247-61, 1998.
• Arruda, A. [1970a]
  Sur les systèmes NFi de Da Costa.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 270, pp. 1081-1084.
• Arruda, A. [1970b]
  Sur les systèmes NF-omega.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 270, pp. 1137-1139.
• Arruda, A. [1971]
  La mathématique classique dans NF-omega.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 272, p. 1152.
• Arruda, A. and Da Costa, N.C.A. [1964]
  Sur une hiérarchie de systèmes formels.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 259, pp. 2943-2945.

• Barwise, J. [1984]
  Situations, sets and the axiom of foundation.
  Logic Colloquium '84, ed. J. Paris, A. Wilkie, and G. Wilmers, North-Holland, pp. 21-36.
• Benes, V.E. [1954]
  A partial model for NF.
  Journal of Symbolic Logic 19, pp. 197-200.
• Boffa, M. [1971]
  Stratified formulas in Zermelo-Fränkel set theory.
  Bulletin de l'Académie Polonaise des Sciences, série Math. 19, pp. 275-280.
• Boffa, M. [1973]
  Entre NF et NFU.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 277, pp. 821-822.
• Boffa, M. [1975a]
  Sets equipollent to their power sets in NF.
  Journal of Symbolic Logic 40, pp. 149-150.
• Boffa, M. [1975b]
  On the axiomatization of NF.
  Colloque international de Logique, Clermont-Ferrand 1975, pp. 157-159.
• Boffa, M. [1977a]
  A reduction of the theory of types.
  Set theory and hierarchy theory, Springer Lecture Notes in Mathematics 619, pp. 95-100.
• Boffa, M. [1977b]
  The consistency problem for NF.
  Journal of Symbolic Logic 42, pp. 215-220.
• Boffa, M. [1977c]
  Modèles cumulatifs de la théorie des types.
  Publications du Département de Mathématiques de l'Université de Lyon 14 (fasc. 2), pp. 9-12.
• Boffa, M. [1981]
  La théorie des types et NF.
  Bulletin de la Société Mathématique de Belgique (série A) 33, pp. 21-31.
• Boffa, M. [1982]
  Algèbres de Boole atomiques et modelès de la théorie des types.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 1-5.
• Boffa, M. [1984a]
  Arithmetic and the theory of types.
  Journal of Symbolic Logic 49, pp. 621-624.
• Boffa, M. [1984b]
  The point on Quine's NF (with a bibliography).
  TEORIA 4 (fasc. 2), pp. 3-13.
• Boffa, M. [1988]
  ZFJ and the consistency problem for NF.
  Jahrbuch der Kurt Gödel Gesellschaft (Wien), pp. 102-106
• Boffa, M. [1989]
  A set theory with approximations.
  Jahrbuch der Kurt Goedel Gesellschaft 1989, p.95-97.
• Boffa, M. [1992]
  Decoration ensembliste de graphes par approximations.
  Cahiers du Centre de Lo- gique (Louvain-la-Neuve), vol.7 (1992), p.45-50.
• Boffa, M. and Casalegno, P. [1985]
  The consistency of some 4-stratified subsystems of NF including NF3.
  Journal of Symbolic Logic 50, pp. 407-411.
• Boffa, M. and Crabbé, M. [1975]
  Les théorèmes 3-stratifiés de NF3.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 280, pp. 1657-1658.
• Boffa, M. and Pétry, A. [1993]
  On self-membered sets in Quine's set theory NF.
  Logique et Analyse 141-142, pp. 59-60.

• Church, A. [1974]
  Set theory with a universal set.
  Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, American Mathematical Society, pp. 297-308.
  Reprinted in International Logic Review 15, pp. 11-23.
• Cocchiarella, N.B. [1976]
  A note on the definition of identity in Quine's New Foundations.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 22, pp. 195-197.
• Cocchiarella, N.B. [1985]
  Frege's double-correlation thesis and Quine's set theories NF and ML
  Journal of Philosophical Logic, vol 14, no. 4: 253-326.
• Cocchiarella, N.B. [1992a]
  Cantor's power-set theorem versus Frege's double-correlation thesis
  History and Philosophy of Logic, vol. 13: 179-201.
• Cocchiarella, N.B. [1992b]
  Conceptual realism versus Quine on classes and higher-order logic,
  Synthese, vol. 90: 379-436.
• Coret, J. [1964]
  Formules stratifiées et axiome de fondation.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 264, pp. 809-812 and 837-839.
• Coret, J. [1970]
  Sur les cas stratifiés du schema de remplacement.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 271, pp. 57-60.
• Crabbé, M. [1975]
  Non-normalisation de ZF
  unpublished (Kiel 1974). Download from www.lofs.ucl.ac.be/log/perso/Crabbe/textes/contreexemple.pdf.
  Note: Marcel says "My old unpublished counterexample to normalisation of ZF might also be of interest..."
• Crabbé, M. [1973]
  NF en un nombre fini d'axiomes.
  Unpublished. Downloadable from here
• Crabbé, M. [1975]
  Types ambigus.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 280, pp. 1-2.
• Crabbé, M. [1976]
  La prédicativité dans les théories élémentaires.
  Logique et Analyse 74-75-76, pp. 255-266.
• Crabbé, M. [1978a]
  Ramification et prédicativité.
  Logique et Analyse 84, pp. 399-419.
• Crabbé, M. [1978b]
  Ambiguity and stratification.
  Fundamenta Mathematicae CI, pp. 11-17.
• Crabbé, M. [1982a]
  On the consistency of an impredicative subsystem of Quine's NF.
  Journal of Symbolic Logic 47, pp. 131-136.
• Crabbé, M. [1982b]
  À propos de 2^alpha.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 17-22.
• Crabbé, M. [1983]
  On the reduction of type theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 29, pp. 235-237.
• Crabbé, M. [1984]
  Typical ambiguity and the axiom of choice.
  Journal of Symbolic Logic 49, pp. 1074-1078.
• Crabbé, M. [1986]
  Le schéma d'ambiguïté en théorie des types.
  Bulletin de la Société Mathématique de Belgique (série B) 38, pp. 46-57.
• Crabbé, M. [1991]
  Stratification and cut-elimination.
  Journal of Symbolic Logic 56, pp. 213-226
• Crabbé, M. [1992a]
  On NFU.
  Notre Dame Journal of Formal Logic 33, pp 112-119.
• Crabbé, M. [1992b]
  Soyons positifs: la complétude de la théorie näive des ensembles.
  Cahiers du Centre de Logique 1992, volume 7, pp.51-68.
• Crabbé, M. [1994]
  The Hauptsatz for stratified comprehension: a semantic proof.
  Mathematical Logic Quarterly 40, pp, 481-489.
• Crabbé, M. [1999]
  L'axiome de l'infini dans NFU.
  C. R. Acad. Sci. Paris, t. 329, Série I, p. 1033-1035, 1999.
• Crabbé,M. [2000]
  On the set of atoms.
  L. J. of the IGPL, Vol. 8, no. 6, pp. 751-759.
• Crabbé,M. [2000]
  The rise and fall of typed sentences
  Journal of Symbolic Logic, vol. 65, no. 4, pp. 1858-1862.
• Curry, H.B. [1954]
  Review of Rosser [1953a].
  Bulletin of the American Mathematical Society 60, pp. 266-272

• Da Costa, N.C.A. [1964]
  Sur une système inconsistent de théorie des ensembles.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 258, pp. 3144-3147.
• Da Costa, N.C.A. [1965a]
  Sur les systèmes formels Ci, Ci*, Ci=, Di et NF.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 260, pp. 5427-5430.
• Da Costa, N.C.A. [1965b]
  On two systems of set theory.
  Proc. Koningl. Nederl. Ak. v. Wetens. (serie A) 68, pp 95-99.
• Da Costa, N.C.A. [1969]
  On a set theory suggested by Dedecker and Ehresmann I and II.
  Proceedings of the Japan Academy 45, pp. 880-888.
• Da Costa, N.C.A. [1971]
  Remarques sur le système NF1.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 272, pp. 1149-1151.
• Da Costa, N.C.A. [1974]
  Remarques sur les Calculs Cn, Cn*, Cn=, et Dn.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 278, pp. 818-821.
• Dzierzgowski, D. [1991]
  Intuitionistic typical ambiguity.
  Archive for Mathematical Logic 31, pp. 171-182.
• Dzierzgowski, D. [1993a]
  Typical ambiguity and elementary equivalence.
  Mathematical Logic Quarterly 39, pp. 436-446.
• Dzierzgowski, D. [1993b]
  Le théorème d'ambiguïté et son extension à la logique intuitionniste.
  Dissertation doctorale. Université catholique de Louvain, Institut de mathématique pure et appliquée.
• Dzierzgowski, D. [1995]
  Models of intuitionistic TT and NF.
  Journal of Symbolic Logic 60, pp. 640-653.
• Dzierzgowski, Daniel[1996]
  Finite sets and natural numbers in intuitionistic TT, Notre Dame Journal of Formal Logic.
  vol. 37, no. 4 (1996), pp. 585-601.
• Dzierzgowski, Daniel[1998]
  Finite sets and natural numbers in intuitionistic TT without extensionality.
  Studia Logica, vol. 61, no. 3 (November 1998), pp. 417-428.

• Enayat, A.[2006]
  From Bounded Arithmetic to Second Order Arithmetic via Automorphisms
  Logic in Tehran, pp. 87--113, Lect. Notes Logic, 26, Assoc. Symbol. Logic, La Jolla, CA
  Note:the author says "includes the core results about automorphisms relevant to NFU + "the universe is finite". The results about NFU are announced in section 5.1 (but see also the introduction)."
• Enayat, Ali[2004]
  Automorphisms, Mahlo Cardinals, and NFU
  in Nonstandard Models of Arithmetic and Set Theory, (Enayat, A. and Kossak, R., eds.), Contemporary Mathematics, vol. 361, American Mathematical Society. Also available here.
• Engeler, E. and Röhrli, H. [1969]
  On the problem of foundations of category theory.
  Dialectica 23, pp. 58-66.
• Esser, Olivier [1996]
  Inconsistency of GPK + AFA.
  Mathematical Logic Quarterly, vol. 42, pp. 104-108.
• Esser, O. [1997]
  An interpretation of ZF and KM in a positive set theory.
  Mathematical Logic Quarterly 43, pp. 369-377.
• Esser, Olivier [1999]
  On the consistency of a positive theory.
  Mathematical Logic Quarterly, vol. 45, no. 1, pp. 105-116.
• Esser, Olivier [2000]
  Inconsistency of the axiom of choice with the positive set theory GPK + infinity.
  Journal of Symbolic Logic, vol. 65, pp. 1911-1916.
• Esser, Olivier [2003]
  On the axiom of extensionality in the positive set theory.
  Mathematical Logic Quarterly, vol. 49, pp. 97-100.
• Esser, Olivier [2003]
  A strong model of paraconsistent logic.
  Notre Dame Journal of Formal Logic, vol. 44.
• Esser, Olivier [2004]
  Une theorie positive des ensembles.
  Cahiers du Centre de Logique, vol. 13, Academia-Bruylant, Louvain-la-Neuve (Belgium), ISBN 2-8729-687-6.
• O. Esser and T. Libert[2005]
  On topological set theory
  Mathematical Logic Quarterly, vol. 51, pp. 263-273.

• Feferman, S. [1972]
  Some formal systems for the unlimited theory of structures and categories.
  Unpublished.
• Forster, T.E. [1976]
  N.F.
  Ph.D. thesis, University of Cambridge.
• Forster, T.E. [1982]
  Axiomatising set theory with a universal set.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 61-76.
• Forster, T.E. [1983a]
  Quine's New Foundations, an introduction.
  Cahiers du Centre de Logique (Louvain-la-neuve) 5. 100 pp.
• Forster, T.E. [1983b]
  Further consistency and independence results in NF obtained by the permutation method.
  Journal of Symbolic Logic 48, pp. 236-238.
• Forster, T.E. [1985]
  The status of the axiom of choice in set theory with a universal set.
  Journal of Symbolic Logic 50, pp. 701-707.
  (The author reports that the definition of "Phi-hat" in this paper is faulty.)
• Forster, T.E. [1987a]
  Permutation models in the sense of Rieger-Bernays.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 33, pp. 201-210.
  (Theorem 2.3 is misstated. The correct version is theorem 3.1.30 of Forster [1992b] and [1995].)
• Forster, T.E. [1987b]
  Term models for weak set theories with a universal set.
  Journal of Symbolic Logic 52, pp. 374-387.
• Forster, T.E. [1989]
  A second-order theory without a (second-order) model.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35, pp. 285-286.
• Forster, T.E. [1992a]
  On a problem of Dzierzgowski.
  Bulletin de la Société Mathématique de Belgique (série B) 44, pp. 207-214.
• Forster, T.E. [1992b]
  Set Theory with a Universal Set.
  Clarendon Press, Oxford.
• Forster, T.E. [1993]
  A semantic characterisation of the well-typed formulae of lambda-calculus.
  Theoretical Computer Science 110, pp 405-408.
• Forster, T.E. [1994] Why Set theory without the axiom of foundation?
  Journal of Logic and Computation, 4, number 4 (August 1994) pp. 333-335.
• Forster, T. E.[1994]
  Weak Systems of Set Theory Related to HOL.
  (Invited talk given at the 1994 meeting of HUG) HUG94, Springer lecture notes in Computer Science vol 859 pp 193-204. Forster advertises that he has a link to this.
• Forster, T.E. [1995]
  Set Theory with a Universal Set, second edition.
  Clarendon Press, Oxford.
• Forster, T. E.[1996]
  (with C.M. Rood.) Sethood and situations.
  Computational Linguistics. 22 (1996) pp 405-408. Thomas advertises a link to this as well.
• Forster, Thomas [1997]
  Quine's NF, 60 years on.
  American Mathematical Monthly, vol. 104, no. 9 (November), pp. 838-845.
• Forster, T.E. and Kaye, R. [1991]
  End-extensions preserving power set.
  Journal of Symbolic Logic 56, pp. 323-328.
  (Errata in Forster [1992b], p. 139; repeated in Forster [1995], p. 152.)
• Forster, T. E.[2001]
  Translation of Specker, E.P. Dualit\"at (Dialektika, 12, pp 451--465; 1957) with a commentary
  in Follesdal, ed: Philosophy of Quine, 4, Logic, Modality and Philosophy of Mathematics pp 7-16. Taylor-and-Francis 2001.

  available on www.dpmms.cam.ac.uk/~tf/duality.ps

• Forster, T. E.[2001]
  Church-Oswald models for Set Theory
  in: Logic, Meaning and Computation: essays in memory of Alonzo Church, Synthese library 305, Kluwer, Dordrecht, Boston and London 2001.
• Forster, T. E.[2001]
  Games played on an illfounded membership relation.
  in A Tribute to Maurice Boffa ed Crabb\'e, Point, and Michaux. (Supplement to the December 2001 number of the Bulletin of the Belgian Mathematical Society)
• Forster, T. E.[2003]
  Reasoning about Theoretical Entities.
  Advances in Logic, vol. 3 World Scientific (UK), Imperial College Press 2003.
• Forster, T. E.[2003]
  ZF + ``Every set is the same size as a wellfounded set
  Journal of Symbolic Logic, 58, (2003) pp 1-4.
• Forster, T. E.[2004]
  AC fails in the natural analogues of $L$ and the cumulative hierarchy that model the stratified fragment of ZF.
  (This was my invited talk for the AMS-MAA joint meeting at Baltimore) in Contemporary Mathematics {\bf 36} 2004. There is a link from Forster's home page as well.
• Forster, T. E.[pending]
  On a paradox of Yablo.
  Logique et Analyse, to appear. Visible on his home page.
• Forti, M. [1987]
  Models of the generalized positive comprehension principle.
  Preprint, Università di Pisa.
• Forti, M. and Hinnion, R. [1989]
  The consistency problem for positive comprehension principles.
  Journal of Symbolic Logic 54, pp. 1401-1418.
• Forti, M. and Honsell, F. [1983]
  Set theory with free construction principles.
  Annali della Scuola Normale Superiore di Pisa, Scienze fisiche e matematiche 10, pp. 493-522.
• M. Forti and F. Honsell.[1989]
  Models of Selfdescriptive Set Theories.
  in Partial Differential equations and the calculus of Variations, Essays in Honor of Ennio De Giorgi, I. (F. Colombini et al., eds), Birkhäuser, Boston (1989), pp. 473-518.
• Forti, M. and Honsell, F. [1992a]
  Weak foundation and anti-foundation properties of positively comprehensive hyperuniverses.
  Cahiers du Centre de Logique (Louvain-la-Neuve) 7, pp. 31-43.
• Forti, M. and Honsell, F. [1992b]
  A general construction of hyperuniverses.
  Preprint, Università di Pisa.
• M. Forti and F. Honsell.[1996]
  Choice Principles in Hyperuniverses.
  Annals of Pure and Applied Logic 77 (1996), pp. 35-52.
• M. Forti and F. Honsell.[1998]
  Addendum and Corrigendum to "Choice Principles in Hyperuniveres".
  Annals of Pure and Applied Logic 92 (1998), pp. 211-214.

• Paul C. Gilmore [1974]
  The Consistency of partial Set Theory without Extensionality.
  Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics, 13, part 2, AMS, Providence RI, pp.147-153.
• Paul C. Gilmore [1986]
  Natural Deduction Based Set Theories: A New Resolution of the Old Paradoxes.
  JSL, Vol.51, pp.393-411.
• Grishin, V.N. [1969]
  Consistency of a fragment of Quine's NF system
  Soviet Mathematics Doklady 10, pp. 1387-1390.
• Grishin, V.N. [1972a]
  The equivalence of Quine's NF system to one of its fragments (in Russian).
  Nauchno-tekhnicheskaya Informatsiya (series 2) 1, pp. 22-24.
• Grishin, V.N. [1972b]
  Concerning some fragments of Quine's NF system (in Russian).
  Issledovania po matematicheskoy lingvistike, matematicheskoy logike i informatsionym jazykam (Moscow), pp. 200-212.
• Grishin, V.N. [1972c]
  The method of stratification in set theory (in Russian).
  Ph.D. thesis, Moscow University.
• Grishin, V.N. [1973a]
  The method of stratification in set theory (Abstract of Ph.D. thesis, in Russian).
  Academy of Sciences of the USSR (Moscow). 9pp.
• Grishin, V.N. [1973b]
  An investigation of some versions of Quine's systems.
  Nauchno-tekhnicheskaya Informatsiya (series 2) 5, pp. 34-37.

• Hailperin, T. [1944]
  A set of axioms for logic.
  Journal of Symbolic Logic 9, pp. 1-19.
• Hatcher, W.S. [1963]
  La notion d'équivalence entre systèmes formels et une généralisation du système dit "New Foundations" de Quine.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 256, pp. 563-566.
• Henson, C.W. [1969]
  Finite sets in Quine's New Foundations.
  Journal of Symbolic Logic 34, pp. 589-596.
• Henson, C.W. [1973a]
  Type-raising operations in NF.
  Journal of Symbolic Logic 38, pp. 59-68.
• Henson, C.W. [1973b]
  Permutation methods applied to NF.
  Journal of Symbolic Logic 38, pp. 69-76.
• Hiller, A.P. and Zimbarg, J.P. [1984]
  Self-reference with negative types.
  Journal of Symbolic Logic 49, pp. 754-773.
• Hinnion, R. [1972]
  Sur les modèles de NF.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 275, p. 567.
• Hinnion, R. [1974]
  Trois résultats concernant les ensembles fortement cantoriens dans les "New Foundations" de Quine.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 279, pp. 41-44.
• Hinnion, R. [1975]
  Sur la théorie des ensembles de Quine.
  Ph.D. thesis, ULB Brussels.
• Hinnion, R. [1976]
  Modèles de fragments de la théorie des ensembles de Zermelo-Fraenkel dans les "New Foundations" de Quine.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 282, pp. 1-3.
• Hinnion, R. [1979]
  Modèle constructible de la théorie des ensembles de Zermelo dans la théorie des types.
  Bulletin de la Société Mathématique de Belgique (série B) 31, pp. 3-11.
• Hinnion, R. [1980]
  Contraction de structures et application à NFU: Définition du "degré de non-extensionalité" d'une relation quelconque.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 290, pp. 677-680.
• Hinnion, R. [1981]
  Extensional quotients of structures and applications to the study of the axiom of extensionality.
  Bulletin de la Société Mathématique de Belgique (série B) 33, pp. 173-206.
• Hinnion, R. [1982]
  NF et l'axiome d'universalité.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 45-59.
• Hinnion, R. [1986]
  Extensionality in Zermelo-Fraenkel set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 32, pp. 51-60.
• Hinnion, R.[1987]
  Le paradoxe de Russell dans des versions positives de la theorie naive des ensembles
  Comptes Rendus de l'Academie des Science de Paris, vol. 304, pp. 307-310.
• Hinnion, R. [1989]
  Embedding properties and anti-foundation in set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35, pp. 63-70.
• Hinnion, R. [1990]
  Stratified and positive comprehension seen as superclass rules over ordinary set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 36, pp. 519-534.
• Hinnion, R.[1994]
  Naive set theory with extensionality in partial logic and in paradoxical logic.
  Notre Dame Journal of Formal Logic, vol. 35, pp. 15-40..
• Hinnion, R.[2003]
  About the coexistence of classical sets with non-classical ones: a survey
  Logic and Logical Philosophy, vol. 11, pp. 79-90.
• Hinnion, R.[2006]
  Intensional positive set theory
  Reports on Mathematical Logic, vol. 40.
• R. Hinnion and T. Libert[2003]
  Positive abstraction and extensionality
  Journal of Symbolic Logic, vol. 68, pp. 828-836.
• Holmes, M.R. [1991a]
  Systems of combinatory logic related to Quine's 'New Foundations.'
  Annals of Pure and Applied Logic 53, pp. 103-133.
• Holmes, M.R. [1991b]
  The Axiom of Anti-Foundation in Jensen's 'New Foundations with Ur-Elements.'
  Bulletin de la Société Mathématique de Belgique (série B) 43, pp. 167-179.
• Holmes, M.R. [1992]
  Modelling fragments of Quine's 'New Foundations.'
  Cahiers du Centre de Logique (Louvain-la-Neuve) 7, pp. 97-112.
• Holmes, M.R. [1993]
  Systems of combinatory logic related to predicative and 'mildly impredicative' fragments of Quine's 'New Foundations.'
  Annals of Pure and Applied Logic 59, pp 45-53.
• Holmes, M.R. [1994]
  The set theoretical program of Quine succeeded (but nobody noticed).
  Modern Logic 4, pp. 1-47.
• Holmes, M.R. [1995a]
  The equivalence of NF-style set theories with "tangled" type theories; the construction of omega-models of predicative NF (and more).
  Journal of Symbolic Logic 60, pp. 178-189.
• Holmes, M.R. [1995b]
  Untyped lambda-calculus with relative typing.
  Typed Lambda-Calculi and Applications (Proceedings of TLCA '95), Springer, pp. 235-248.
• Holmes, M. R. [1998]
  Elementary set theory with a universal set.
  volume 10 of the Cahiers du Centre de logique, Academia, Louvain-la-Neuve (Belgium), 241 pages, ISBN 2-87209-488-1. See here for an on-line errata slip. By permission of the publishers, a corrected text is published online here; an official second edition will appear online eventually.
• Holmes, M. R.[1999]
  Subsystems of Quine's ``New Foundations'' with Predicativity Restrictions
  Notre Dame Journal of Formal Logic, vol. 40, no. 2, pp. 183-196.
  appeared physically in 2001.
• Holmes, M. R. and Alves-Foss, J.[2000]
  A strong and mechanizable grand logic.
  in Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, Lecture Notes in Computer Science, vol. 1869, Springer-Verlag, pp. 283-300.
  This is the theoretical paper on the foundations of the Watson theorem prover.
• Holmes, M. R.[2001]
  Foundations of mathematics in polymorphic type theory.
  Topoi, vol. 20, pp. 29-52.
  NOTE: this is my official answer to the claim by certain parties on the FOM list that mathematics must be defined in terms of what we can do in ZFC...
• Holmes, M. R.[2001]
  Strong axioms of infinity in NFU.
  Journal of Symbolic Logic, vol. 66, no. 1, pp. 87-116.
  (brief notice of errata with corrections to appear in a future issue).
• Holmes, M. R.[2001]
  The Watson theorem prover.
  Journal of Automated Reasoning, vol. 26, no. 4, pp. 357-408.
  This paper describes a theorem prover using a higher order logic based on NFU.
• Holmes, M. R.[2001]
  Tarski's Theorem and NFU
  in C. Anthony Anderson and M Zeleny (eds.), Logic, Meaning and Computation, Kluwer, 2001, pp. 469--478.
• Holmes, M. R.[2002]
  Forcing in NFU and NF
  in M. Crabbe, C. Michaux, and F. Point, eds., A tribute to Maurice Boffa, Belgian Mathematical Society, 2002.
• Holmes, M. R.[2004]
  Paradoxes in double extension set theories
  Studia Logica, vol. 77 (2004), pp. 41-57.
• Holmes, M. R.[2005]
  The structure of the ordinals and the interpretation of ZF in double extension set theory
  Studia Logica, vol. 79, pp. 357-372.

• Jamieson, M.W. [1994]
  Set theory with a Universal Set.
  Ph.D. thesis, University of Florida. 114pp.
• Jech, T. [1995]
  OTTER experiments in a system of combinatory logic
  Journal of Automated Reasoning, 14, pp. 413-426.
• Jensen, R.B. [1969]
  On the consistency of a slight(?) modification of Quine's NF.
  Synthese 19, pp. 250-263.

• Kaye, R.W. [1991]
  A generalisation of Specker's theorem on typical ambiguity.
  Journal of Symbolic Logic 56, pp 458-466.
• Kaye, R.W. [1996]
  The quantifier complexity of NF.
  Bulletin of the Belgian Mathematical Societ y Simon Stevin, ISSN 1370-1444, 3, pp 301-312.
• Kemeny, J.G. [1950]
  Type theory vs. set theory (abstract).
  Journal of Symbolic Logic 15, p. 78.
• Kirmayer, G. [1981]
  A refinement of Cantor's theorem.
  Proceedings of the American Mathematical Society 83, p. 774.
• Kisielewicz, Andrzej[1989]
  Double extension set theory
  Reports on Mathematical Logic 23:81--89, 1989.
• Kisielewicz, Andrzej[1998]
  A very strong set theory?
  Studia Logica 61:171--178, 1998.
  Note: as I comment above, the jury is still out on double extension set theory; but if the remaining version of the 1998 paper is consistent it is certainly appropriate here.
• Körner, F. [1994]
  Cofinal indiscernibles and some applications to New Foundations.
  Mathematical Logic Quarterly 40, pp. 347-356.
• Körner, F. [1998]
  Automorphisms moving all non-algebraic points and an application to NF.
  Journal of Symbolic Logic 63, p. 815-830.
• Kühnrich, M. and Schultz, K. [1980]
  A hierarchy of models for Skala's set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 26, pp. 555-559.
• Kuzichev, A.C. [1981]
  Arithmetic theories constructed on the basis of lambda-conversion.
  Soviet Mathematics Doklady 24, pp. 584-589.
• Kuzichev, A.C. [1983]
  Nyeprotivoretchivost' Sistema NF Quine.
  Doklady Akademia Nauk 270, pp. 537-541.

• Lake, J. [1974]
  Some topics in set theory.
  Ph.D. thesis, Bedford College, London University.
• Lake, J. [1975]
  Comparing type theory and set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 21, pp. 355-356.
• Libert, T.[2004]
  Semantics for naive set theory in many-valued logics, technique and historical account
  in, J. van Benthem and G. Heintzmann, eds., The age of alternative logics, Kluwer, 2004.
• Libert, T.[2005]
  Models for a Paraconsistent Set Theory
  Journal of Applied Logic, vol. 3, pp. 15-41.
• Libert, T.[2006 -- I believe this means "yet to appear"]
  More studies on the axiom of comprehension
  Cahiers du Centre de Logique, no. 15, Academia-Bruylant, Louvain-la-Neuve (Belgium).
• O. Esser and T. Libert[2005]
  On topological set theory
  Mathematical Logic Quarterly, vol. 51, pp. 263-273.
• R. Hinnion and T. Libert[2003]
  Positive abstraction and extensionality
  Journal of Symbolic Logic, vol. 68, pp. 828-836.

• McLarty, C. [1992]
  Failure of cartesian closedness in NF.
  Journal of Symbolic Logic 57, pp. 555-556.
• McNaughton, R. [1953]
  Some formal relative consistency proofs.
  Journal of Symbolic Logic 18, pp. 136-144.
• Malitz, R.J. [1976]
  Set theory in which the axiom of foundation fails.
  Ph.D. thesis, UCLA.
• Manakos, J. [1984]
  On Skala's set theory.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 30, pp. 541-546.
• Mitchell, E. [1976]
  A model of set theory with a universal set.
  Ph.D. thesis, University of Wisconsin, Madison, Wisconsin.

• Oberschelp, A. [1964]
  Eigentliche Klasse als Urelemente in der Mengenlehre.
  Mathematische Annalen 157, pp. 234-260.
• Oberschelp, A. [1973]
  Set theory over classes.
  Dissertationes Mathematicae 106. 62 pp.
• Oksanen, M.[1999]
  The Russell-Kaplan Paradox and Other Modal Paradoxes: A New Solution
  Nordic Journal of Philosophical Logic, Vol. 4, No. 1, pp. 73-93, June 1999, Scandinavian University Press.
  Also available on- line at http://www.hf.uio.no/filosofi/njpl/
• Orey, S. [1955]
  Formal development of ordinal number theory.
  Journal of Symbolic Logic 20, pp. 95-104.
• Orey, S. [1956]
  On the relative consistency of set theory.
  Journal of Symbolic Logic 21, pp. 280-290.
• Orey, S. [1964]
  New Foundations and the axiom of counting.
  Duke Mathematical Journal 31, pp. 655-660.
• Oswald, U. [1976]
  Fragmente von "New Foundations" und Typentheorie.
  Ph.D. thesis, ETH Zürich. 46 pp.
• Oswald, U. [1981]
  Inequivalence of the fragments of New Foundations.
  Archiv für mathematische Logik und Grundlagenforschung 21, pp. 77-82.
• Oswald, U. [1982]
  A decision method for the existential theorems of NF2.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 23-43.
• Oswald, U. and Kreinovich, V. [1982]
  A decision method for the Universal sentences of Quine's NF.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 28, pp. 181-187.

• Pabion, J.F. [1980]
  TT3I est équivalent à l'arithmétique du second ordre.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 290, pp. 1117-1118.
• Pétry, A. [1974]
  À propos des individus dans les "New Foundations" de Quine.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 279, pp. 623-624.
• Pétry, A. [1975]
  Sur l'incomparabilité de certains cardinaux dans le "New Foundations" de Quine.
  Comptes Rendus hebdomadaires des séances de l'Académie des Sciences de Paris (série A) 281, pp. 673-675.
• Pétry, A. [1976]
  Sur les cardinaux dans le "New Foundations" de Quine.
  Ph.D. thesis, University of Liège. 66 pp.
• Pétry, A. [1977]
  On cardinal numbers in Quine's NF.
  Set theory and hierarchy theory, Springer Lecture Notes in Mathematics 619, pp. 241-250.
• Pétry, A. [1979]
  On the typed properties in Quine's NF.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25, pp. 99-102.
• Pétry, A. [1982]
  Une charactérisation algébrique des structures satisfaisant les mêmes sentences stratifiées.
  Cahiers du Centre de Logique (Louvain-la-neuve) 4, pp. 7-16.
• Pétry, A. [1992]
  Stratified languages.
  Journal of Symbolic Logic 57, pp. 1366-1376.
• Prati, N. [1994]
  A partial model of NF with E.
  Journal of Symbolic Logic 59, pp. 1245-1253.

• Quine, W.V. [1937a]
  New foundations for mathematical logic.
  American Mathematical Monthly 44, pp. 70-80.
  Reprinted in Quine [1953a]
• Quine, W.V. [1937b]
  On Cantor's theorem.
  Journal of Symbolic Logic 2, pp. 120-124.
• Quine, W.V. [1945]
  On ordered pairs.
  Journal of Symbolic Logic 10, pp. 95-96.
• Quine, W.V. [1951a]
  Mathematical logic, revised ed.
  Harvard University Press.
• Quine, W.V. [1951b]
  On the consistency of "New Foundations."
  Proceedings of the National Academy of Sciences of the USA 37, pp. 538-540.
• Quine, W.V. [1953a]
  From a logical point of view.
  Harper & Row.
• Quine, W.V. [1953b]
  On omega-inconsistency and a so-called axiom of infinity.
  Journal of Symbolic Logic 18, pp. 119-124.
  Reprinted in Quine [1966].
• Quine, W.V. [1963]
  Set theory and its logic.
  Belknap Press.
• Quine, W.V. [1966]
  Selected logic papers.
  Random House.
• Quine, W.V. [1969]
  Set theory and its logic, revised edition.
  Belknap Press.
• Quine, W.V. [1993]
  The inception of NF.
  Bulletin de la Société Mathématique de Belgique (série B) 45, pp. 325-328.

• Rosser, J.B. [1939a]
  On the consistency of Quine's new foundations for mathematical logic.
  Journal of Symbolic Logic 4, pp. 15-24.
• Rosser, J.B. [1939b]
  Definition by induction in Quine's new foundations for mathematical logic.
  Journal of Symbolic Logic 4, p. 80.
• Rosser, J.B. [1942]
  The Burali-Forti paradox.
  Journal of Symbolic Logic 7, pp. 11-17.
• Rosser, J.B. [1952]
  The axiom of infinity in Quine's New Foundations.
  Journal of Symbolic Logic 17, pp. 238-242.
• Rosser, J.B. [1953a]
  Logic for mathematicians.
  McGraw-Hill.
• Rosser, J.B. [1953b]
  Deux esquisses de logique.
  Paris.
• Rosser, J.B. [1954]
  Review of Specker [1953].
  Journal of Symbolic Logic 19, p. 127.
• Rosser, J. B. [1956]
  The relative strength of Zermelo's set theory and Quine's new foundations.
  Proceedings of the International Congress of Mathematicians (Amsterdam 1954) III, pp. 289-294.
• Rosser, J. B. [1978]
  Logic for mathematicians, second edition.
  Chelsea Publishing.
• Rosser, J.B. and Wang, H. [1950]
  Non-standard models for formal logic.
  Journal of Symbolic Logic 15, pp. 113-129.
• Russell, B.A.W. [1908]
  Mathematical logic as based on the theory of types.
  American Journal of Mathematics 30, pp. 222-262.

• Schultz, K. [1977]
  Ein Standardmodell für Skala's Mengenlehre.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 23, pp. 405-408.
• Schultz, K. [1980]
  The consistency of NF.
  Unpublished.
• Scott, D.S. [1960]
  Review of Specker [1958].
  Mathematical Reviews 21, p. 1026.
• Scott, D.S. [1962]
  Quine's individuals.
  Logic, methodology and philosophy of science, ed. E. Nagel, Stanford University Press, pp. 111-115.
• Scott, D.S. [1980]
  The lambda calculus: some models, some philosophy.
  The Kleene Symposium, North-Holland, pp. 116-124.
• Sheridan, K.J. [199?]
  The singleton function is a set in a slight extension of Church's set theory.
  Ph.D thesis, University of Oxford.
• Skala, H. [1974a]
  Eine neue Methode, die Paradoxien der naiven Mengenlehre zu vermeiden.
  Annalen der Österreichen Akademie der Wissenschaften Math-Nat. Kl. II, pp. 15-16.
• Skala, H. [1974b]
  An alternative way of avoiding the set-theoretical paradoxes.
  Zeitschrift für mathematische Logik und Grundlagen der Mathematik 20, pp. 233-237.
• Specker, E.P. [1953]
  The axiom of choice in Quine's new foundations for mathematical logic.
  Proceedings of the National Academy of Sciences of the USA 39, pp. 972-975. See this link (if accessible).
• Specker, E.P. [1958]
  Dualität.
  Dialectica 12, pp. 451-465.
  Note: There is a translation of this by Forster listed elsewhere in this document: available on www.dpmms.cam.ac.uk/~tf/duality.ps

• Specker, E.P. [1962]
  Typical ambiguity.
  Logic, methodology and philosophy of science, ed. E. Nagel, Stanford University Press, pp. 116-123.
• Stanley, R.L. [1955]
  Simplified foundations for mathematical logic.
  Journal of Symbolic Logic 20, pp. 123-139.

• Vayl, V.
  Gentzen systems of postulates for set theory.
  AMS translations series 2 vol. 135 pp. 23-37.

• Wang, H. [1950]
  A formal system of logic.
  Journal of Symbolic Logic 15, pp. 25-32.
• Wang, H. [1952]
  Negative types.
  MIND 61, pp. 366-368.
• Wang, H. [1953]
  The categoricity question of certain grand logics.
  Mathematische Zeitschrift 59, pp. 47-56.
• Weydert, E. [1989]
  How to approximate the naïve comprehension scheme inside of classical logic.
  Ph.D. thesis, Friedrich-Wilhelms-Universität Bonn.
  Bonner mathematische Schriften 194.
• Whitehead, A.N. and Russell, B.A.W. [1910]
  Principia mathematica. Cambridge University Press.