论文标题
关于钢和钢的问题
On a question of Slaman and Steel
论文作者
论文摘要
我们考虑了一个古老的Slaman and Steel问题：Turing等效性是否是Borel等效关系的增加，其中没有一个包含均匀计算的无限序列。我们表明，这个问题与马丁的猜想以及可数鲍尔的等效关系密切相关。特别是，如果Slaman and Steel的问题具有积极的答案，则意味着存在一个通用的可计数borel等效性，并不统一地通用，并且有一个$（\ equiv_t，\ equiv_m）$ - 不变函数 - 在任何尖锐的完美设置上都不均匀地不变。
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.
