Three faculty investigators and their graduate students are involved in this project. Martin and Steel will work in set theory. Steel, and Martin to some extent, will concentrate on inner model theory and on strong forms of determinacy. Martin also expects to complete his monograph on proofs of determinacy. Moschovakis will work in the theory of algorithms and its applications to the foundations of mathematical computer science. Set theory lies at the foundation of all mathematics. Important questions concern the axioms that underly all number systems, algebra, geometry and analysis. Are certain axioms necessary? Are they irrelevant in certain contexts? Particularly significant in this regard is the so-called Axiom of Determinacy, which can be framed as a statement that a certain two-person game has a winning strategy for one player or the other. The game in question involves constructing a set by having the two players alternate in selecting members for it.
