Mathematical Sciences: Recursion Theory and Set Theory

小行星9505153 马丁将在集合论和描述集合论，特别是确定性假设，他的首要目标是完成他期待已久的 从大基数公理证明确定性的研究专著。 斯蒂尔也将在集合论和描述性集合论方面工作， 更具体地说，在建设和研究规范，内部 满足指定大基数或确定性的ZFC模型 假设。 Moschovakis将致力于定点递归及其 计算理论的应用，包括数学 递归算法的建模，递归定义的逻辑，以及 中递归方程标准解的构造 非确定性和并发设置。 该补助金的主要研究人员一直是重塑古典集合论基础的关键贡献者之一， 数学在过去的二十五年里，与介绍和 研究关于集合的新假设，这些假设使得解决许多问题成为可能。 关于真实的数字的长期悬而未决的问题。 马丁和斯蒂尔 继续致力于这一基本计划，寻求扩大它， 描述它的局限性。 Moschovakis改变兴趣大约十年 他目前的研究计划旨在提供一个严格的， 计算机科学的数学基础 一个主要的终极目标 他的工作之一是构建一个“程序逻辑”， 计算机系统的开发和验证。 ***

9505153 Martin Martin will work in set theory and descriptive set theory, especially determinacy hypotheses, and his first goal is to complete his long-awaited research monograph on proofs of determinacy from large cardinal axioms. Steel will also work generally in set theory and descriptive set theory, and more specifically on the construction and study of canonical, inner models of ZFC that satisfy specified large cardinal or determinacy assumptions. Moschovakis will work on fixpoint recursion and its applications to the theory of computation, including the mathematical modeling of recursive algorithms, the logic of recursive definitions, and the construction of canonical solutions for recursive equations in non-deterministic and concurrent settings. The Principal Investigators of this Grant have been among the key contributors to the reshaping of the classical, set-theoretic foundations of mathematics during the last twenty-five years, with the introduction and study of new hypotheses about sets that have made it possible to solve many long-standing, open problems about the real numbers. Martin and Steel will continue working on this fundamental program, seeking to extend it and to delineate its limitations. Moschovakis changed interests about ten years ago, and his current research program aims to provide a rigorous, mathematical foundation for computer science. One of the main, ultimate aims of his work is to construct a "logic of programs" that will be useful in the development and verification of computing systems. ***