Mathematical Sciences: Aspects of Computability

Slaman参与了几个项目，旨在阐明 计算的动态性、可计算的结构、 集合和可计算性概念之间的联系 不同的环境。 他计划在不同的研究中， 算术;图灵度;全局和局部问题;递归 以及复杂性理论。 这种性质的研究涉及一种理想化的形式， 计算不受内存大小或实际时间限制的限制。 在这方面取得积极成果可能不切实际。 有意义的，但负面的结果，当然，仍然是完美的， 有意义的 他们构成不可能的证据，在非常 强烈感觉到，即使是不合理的巨大内存和不合理的 冗长的计算运行将是不够的。

Slaman is engaged in several projects designed to illuminate the dynamic feature of computation, the structure of computable sets and the connection between notions of computability in varying environments. He plans separate studies in fragments of arithmetic; Turing degrees, global and local questions; recursion in higher types; and complexity theory. Investigations of this nature concern an idealized form of computing unlimited by memory size or practical time constraints. Positive results in this context may not be practically meaningful, but negative results, of course, are still perfectly meaningful. They constitute impossibility proofs in the very strong sense that even unreasonably huge memory and unreasonably lengthy computation runs will not suffice.