Department of Mathematics
Selection principles and infinite games
Liljana Babinkostova
Boise State University
Cantor's diagonal argument is one of the classical tools of set theory. In classical literature several measure-like properties, basis properties or covering properties have been defined in terms of diagonalization processes. The area of selection principles unifies these studies by showing that each of these properties can be characterized by a typical diagonalization process, called a selection principle. Selection principles have natural infinite games associated with them. These games are powerful tools for developing the theory of these selection principles. In this talk we survey the selection principles S1(A,B), Sfin(A,B) and Sc(A,B) and their associated games. We show how they are related to basis properties, measure like properties, and also to Lebesgue's covering dimension. We present some recent results in connection with the questions whether the Sierpinski basis property implies the Rothberger property, whether the product of a strictly o-bounded group and an o-bounded group is o-bounded and when finite powers of Haver spaces are Haver spaces.
All interested persons are welcome.
The talk will be accessible to upper class students.