Solovay reducibility implies S2a-reducibility
Logic
2024-08-09 v1
Abstract
The original notion of Solovay reducibility was introduced by Robert M. Solovay (unpublished notes) in 1975 as a measure of relative randomness.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.
Cite
@article{arxiv.2408.04074,
title = {Solovay reducibility implies S2a-reducibility},
author = {Ivan Titov},
journal= {arXiv preprint arXiv:2408.04074},
year = {2024}
}