索洛维还原性意味着 S2a 还原性

arXiv - MATH - Logic Pub Date : 2024-08-07 DOI:arxiv-2408.04074

Ivan Titov

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引用次数: 0

摘要

索洛维可还原性的最初概念是由罗伯特-索洛维（Robert M.Solovay）（未发表的笔记）于1975年提出的，作为一种相对随机性的度量。郑锡忠和罗伯特-雷廷格（DOI:10.1007/978-3-540-27798-9_39）于 2004 年提出的 S2a-reducibility 是对索洛维可简化性的修改，适用于可计算近似（c.a. ）的实数。我们证明了索洛维可简化性意味着 c.a. 复数集上的 S2a 可简化性，即使使用同一个常数也是如此，反之亦然。

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Solovay reducibility implies S2a-reducibility

The original notion of Solovay reducibility was introduced by Robert M. Solovay (unpublished notes) in 1975 as a measure of relative randomness.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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arXiv - MATH - Logic

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