关于Slaman和Steel的一个问题
On a question of Slaman and Steel
AI总结：
本文探讨了Slaman和Steel关于图灵等价是否可分解为不包含可计算无限序列的可测等价关系的递增并集的问题，并将其与Martin猜想及可数可测等价关系联系起来。
摘要：
我们考虑一个由Slaman和Steel提出的老问题：图灵等价是否是不包含任何可计算无限序列的可测等价关系的递增并集。我们证明这个问题与Martin猜想周围的问题以及可数可测等价关系密切相关。特别是，如果Slaman和Steel的问题有肯定答案，它将意味着存在一个非均匀 universal 的可数可测等价关系，且存在一个在（≡_T，≡_m）下不变但不在任何定点完美集上均匀不变的函数。
英文摘要：
We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infinite sequence. We show this question is deeply connected to problems surrounding Martin's conjecture, and also in countable Borel equivalence relations. In particular, if Slaman and Steel's question has a positive answer, it implies there is a universal countable Borel equivalence which is not uniformly universal, and that there is a $(\equiv_T,\equiv_m)$-invariant function which is not uniformly invariant on any pointed perfect set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
