Series: Penn State Logic Seminar Date: Tuesday, April 27, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: Vijay Krishna, Penn State, Economics Title: Set Theory Without the Axiom of Foundation -- An Application to Game Theory Abstract: A game of incomplete information is a game where there is some uncertainty about the structure of the game. The standard formalisation of such a situation introduces the notions of "type" of a player and "universal belief space". In this talk we shall describe the notions of type and universal belief space and define them using using Kolmogoroff's extension theorem. We shall then describe another, more intuitive definition which uses Set Theory without the Axiom of Foundation.