r‐Maximal sets and Q1,N‐reducibility

Mathematical Logic Quarterly 67 (2):138-148 (2021)
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Abstract

We show that if M is an r‐maximal set, A is a major subset of M, B is an arbitrary set and, then. We prove that the c.e. ‐degrees are not dense. We also show that there exist infinite collections of ‐degrees and such that the following hold: (i) for every i, j,, and,(ii) each consists entirely of r‐maximal sets, and(iii) each consists entirely of non‐r‐maximal hyperhypersimple sets.

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Q1-degrees of c.e. sets.R. Sh Omanadze & Irakli O. Chitaia - 2012 - Archive for Mathematical Logic 51 (5-6):503-515.
Hyperhypersimple sets and Q1 -reducibility.Irakli Chitaia - 2016 - Mathematical Logic Quarterly 62 (6):590-595.
Strong Enumeration Reducibilities.Roland Sh Omanadze & Andrea Sorbi - 2006 - Archive for Mathematical Logic 45 (7):869-912.
On subcreative sets and S-reducibility.John T. Gill & Paul H. Morris - 1974 - Journal of Symbolic Logic 39 (4):669-677.

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