Mathematical Sciences: Recursion Theory and Set Theory

三名研究人员和他们的研究生是 参与了这个项目。 马丁和斯蒂尔将在片场工作 理论 斯蒂尔和马丁在某种程度上将专注于 内模理论和强形式的决定性。 马丁还 期望完成他关于确定性证明的专著。 Moschovakis将在算法理论及其 应用于数学计算机科学的基础。 集合论是所有数学的基础。 重要的问题涉及所有数的基本公理 系统、代数、几何和分析。 某些公理 有必要吗？ 在某些情况下，它们是无关紧要的吗？ 特别 在这方面重要的是所谓的确定性公理， 这可以说是一个两人博弈 都有一个获胜的策略 游戏 这个问题涉及到让两个参与人 候补委员为之选任。

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.