Mathematical Sciences: Logical Issues in Constructive Mathematics, and Metamathematics of Algebra

斯考克罗夫特的工作，在数理逻辑，将集中在 建设性的真实的代数，模型理论的p-adic领域，和 证明理论在代数中的应用 找到了一个有效的测试， 命题，在真实的代数，一个有限的逻辑复杂性， 斯考克罗夫特希望为这些问题分离出一组方便的公理 建设性的真实命题。 根据这些公理，他会 我喜欢用模型来证明构造性真实的代数中的定理- 理论手段。 斯考克罗夫特还想知道是否首先- Dana Scott直觉模型中的序真实的代数 分析是递归不可判定的。 最近的工作subanalytic 设置可能允许斯考克罗夫特扩展他的有效测试， 命题的建构性真理， 超越函数 在p-adic场的模型理论中，斯考克罗夫特计划 研究可定义等价关系的性质， 一阶语言之间表达能力的差异 通常用于描述p-adic字段，以及可能的扩展 Kochen关于整定有理函数的定理 斯考克罗夫特希望应用证据理论的论点，以获得 的大小的连续递归或初等界限， Kochen定理给出的恒等式。

Scowcroft's work, in mathematical logic, will center on constructive real algebra, the model theory of p-adic fields, and applications of proof theory to algebra. Having found an effective test for the constructive truth of propositions, in real algebra, of a bounded logical complexity, Scowcroft hopes to isolate a convenient set of axioms for these constructively true propositions. Given such axioms, he would like to prove theorems in constructive real algebra by model- theoretic means. Scowcroft also wants to learn whether first- order real algebra in Dana Scott's model for intuitionistic analysis is recursively undecidable. Recent work on subanalytic sets may allow Scowcroft to extend his effective test for constructive truth to propositions involving certain transcendental functions. In the model theory of p-adic fields, Scowcroft plans to study the properties of definable equivalence relations, the differences in expressive power between the first-order languages commonly used to describe a p-adic field, and possible extensions of Kochen's theorem on integral-definite rational functions. Scowcroft hopes to apply proof-theoretic arguments to obtain primitive-recursive or elementary bounds for the size of the identities given by Kochen's theorem.