Solovay 可归约性蕴含 S2a-可归约性
Solovay reducibility implies S2a-reducibility
AI总结：
本文证明在可计算逼近实数集合上，Solovay 可归约性蕴含 S2a-可归约性且常数相同，但反向蕴含不成立。
摘要：
Solovay 可归约性的原始概念由 Robert M. Solovay 于 1975 年（未发表笔记）引入，作为相对随机性的度量。Xizhong Zheng 和 Robert Rettinger 于 2004 年引入的 S2a-可归约性（DOI:10.1007/978-3-540-27798-9_39）是对 Solovay 可归约性的一种修改，适用于可计算逼近（c.a.）实数。我们证明，在 c.a. 实数集合上，Solovay 可归约性蕴含 S2a-可归约性，甚至具有相同的常数，但反之不成立。
英文摘要：
The original notion of Solovay reducibility was introduced by Robert M. Solovay (unpublished notes) in 1975 as a measure of relative randomness. The S2a-reducibility introduced by Xizhong Zheng and Robert Rettinger (DOI:10.1007/978-3-540-27798-9_39) in 2004 is a modification of Solovay reducibility suitable for computably approximable (c.a.) reals. We demonstrate that Solovay reducibility implies S2a-reducibility on the set of c.a. reals, even with the same constant, but not vice versa.
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