Mathematical Sciences: Set Theory

集合论是所有数学的基础。奠定集合论基础的两个主要途径要么依赖于假设大基数的公理，要么依赖于关于所谓集合论博弈的确定性的各种公理。Woodin将研究大基数与确定性之间的关系，确定性背景下的描述性集合理论，以及在非常大的基数存在下实数良序的可定义性的可能性。他还打算研究图灵度的整体结构和更一般的度结构。最基本的问题是刚性。

Set theory underlies all of mathematics. The two main avenues to laying the foundations of set theory rely either on axioms postulating large cardinal numbers or on various axioms about the determinacy of so-called set theoretic games. Woodin will investigate the relationship between large cardinals and determinacy, descriptive set theory in the context of determinacy, and the possibilities for the definability of the well-ordering of the reals in the presence of very large cardinals. He also intends to investigate the global structure of the Turing degrees and of more general degree structures. The basic question concerns rigidity.