Set Theory at Boise State
The department members who do research in Set Theory are Liljana Babinkostova, Andrés Caicedo, Randall Holmes, Billy Hudson and Marion Scheepers.
From August 2009 to March 30, 2010 we will host a visiting researcher, Dr. Masaru Kada, from Osaka Prefecture University in Japan.
Seminar:
The set theory and logic seminar meets every week to discuss our ongoing research and the research of others in our field. Students are welcome to attend.
Fall 2008 Schedule
Spring 2009 Schedule
Fall 2009 Schedule
Boise Extravaganza in Set Theory:
The set theory conference BEST has been hosted by set theorists at Boise State University since 1992. BEST 18 was hosted during March 27 - 29, 2009.
Set Theory Graduate Courses:
The Department of Mathematics offers a master's degree in mathematics. More information can be found at this link. Set Theory and related courses available through this program include:
Caicedo's Notes for the Fall 2009 edition of MATH 502.
Caicedo's Notes for the Spring 2009 edition of MATH 580.
Geschke's Notes for the Spring 2008 edition of Math 580
Holmes' Notes for the Spring 2008 edition of Math 502.
Set Theory Graduate Students:
Our Individual Set Theory Interests:
Liljana Babinkostova's set theory research interests include set theoretic topology, covering properties, topological games and covering dimension.
Andrés Caicedo's set theory research interests include forcing axioms, large cardinals, and inner models. He is also interested in finite combinatorics and its interaction with mathematical logic.
Randall Holmes has parallel research programs in computer assisted reasoning and in set theories and other logical systems related to Quine's "New Foundations" (NF), especially Jensen's set theory NFU. In computer assisted reasoning, Holmes has developed the Watson theorem prover, an interactive equational theorem prover which uses a stratified lambda-calculus related to NFU as its higher order logic, and also embodies unusual approaches to rewriting and to the use of expressions defined by cases. Other current projects in this area include the development of a complete polymorphic type checker for the ramified type theory of Russell and Whitehead's Principia, and a sequent calculus prover for NFU based on a system defined by Marcel Crabbe. In the pure set theory area, recent investigations have been in the area of strong axioms of infinity suitable to be adjoined to NFU, and their relationship with strong axioms of infinity usually adjoined to ZFC. He recently wrote a paper on the philosophical question as to whether it is possible to present NFU as an independently motivated foundation for mathematics. Holmes is in the planning stages of writing a monograph on the consistent subsystems of NF.
Billy Hudson's interests are in the history and philosophy of mathematical foundations, especially formalism, logicism, and intuitionism, with a particular interest in the history and philosophy of set theory. Billy is currently studying Godel's and Tarski's formalism, Brouwer's intuitionism, and Frege's and Russell's logicism framed in Husserl's phenomenology.
Marion Scheepers' set theory research interests include combinatorics, game theory and Ramsey theory.
The department members who do research in Set Theory are Liljana Babinkostova, Andrés Caicedo, Randall Holmes, Billy Hudson and Marion Scheepers.
From August 2009 to March 30, 2010 we will host a visiting researcher, Dr. Masaru Kada, from Osaka Prefecture University in Japan.
Seminar:
The set theory and logic seminar meets every week to discuss our ongoing research and the research of others in our field. Students are welcome to attend.
Fall 2008 Schedule
Spring 2009 Schedule
Fall 2009 Schedule
Boise Extravaganza in Set Theory:
The set theory conference BEST has been hosted by set theorists at Boise State University since 1992. BEST 18 was hosted during March 27 - 29, 2009.
Set Theory Graduate Courses:
The Department of Mathematics offers a master's degree in mathematics. More information can be found at this link. Set Theory and related courses available through this program include:
- MATH 502: Logic and Set Theory
- MATH 580: Topics in Set Theory
- MATH 581: Topics in Logic
Caicedo's Notes for the Fall 2009 edition of MATH 502.
Caicedo's Notes for the Spring 2009 edition of MATH 580.
Geschke's Notes for the Spring 2008 edition of Math 580
Holmes' Notes for the Spring 2008 edition of Math 502.
Set Theory Graduate Students:
| Student |
Master's Thesis Title |
Year defended |
Advisor |
|
Billy Hudson |
Spring 2007 |
||
|
Trevor Jack |
Incomparable metrics on the Cantor space. |
Spring 2008 |
Our Individual Set Theory Interests:
Liljana Babinkostova's set theory research interests include set theoretic topology, covering properties, topological games and covering dimension.
Andrés Caicedo's set theory research interests include forcing axioms, large cardinals, and inner models. He is also interested in finite combinatorics and its interaction with mathematical logic.
Randall Holmes has parallel research programs in computer assisted reasoning and in set theories and other logical systems related to Quine's "New Foundations" (NF), especially Jensen's set theory NFU. In computer assisted reasoning, Holmes has developed the Watson theorem prover, an interactive equational theorem prover which uses a stratified lambda-calculus related to NFU as its higher order logic, and also embodies unusual approaches to rewriting and to the use of expressions defined by cases. Other current projects in this area include the development of a complete polymorphic type checker for the ramified type theory of Russell and Whitehead's Principia, and a sequent calculus prover for NFU based on a system defined by Marcel Crabbe. In the pure set theory area, recent investigations have been in the area of strong axioms of infinity suitable to be adjoined to NFU, and their relationship with strong axioms of infinity usually adjoined to ZFC. He recently wrote a paper on the philosophical question as to whether it is possible to present NFU as an independently motivated foundation for mathematics. Holmes is in the planning stages of writing a monograph on the consistent subsystems of NF.
Billy Hudson's interests are in the history and philosophy of mathematical foundations, especially formalism, logicism, and intuitionism, with a particular interest in the history and philosophy of set theory. Billy is currently studying Godel's and Tarski's formalism, Brouwer's intuitionism, and Frege's and Russell's logicism framed in Husserl's phenomenology.
Marion Scheepers' set theory research interests include combinatorics, game theory and Ramsey theory.
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