Mathematical Sciences: Aspects of Computability

Slaman参与了几个项目，旨在阐明计算的动态特征，可计算集的结构以及不同环境中可计算性概念之间的联系。他计划在算术的碎片上进行单独的研究；图灵学位，全球和本地问题；高级类型的递归；以及复杂性理论。这种性质的研究涉及不受内存大小或实际时间限制的理想化计算形式。在这种情况下，积极的结果可能没有实际意义，但消极的结果当然仍然是完全有意义的。它们在非常强烈的意义上构成了不可能的证明，即使是不合理的巨大内存和不合理的长计算运行也不够。

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.