Q1-degrees of c.e. sets

Archive for Mathematical Logic 51 (5-6):503-515 (2012)
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Abstract

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q1-degrees linearly ordered under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leq_{Q_1}}$$\end{document} with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q1-degrees are not an upper semilattice. The main result of this paper is that the Q1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document}s1-degrees.

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Citations of this work

Degree structures of conjunctive reducibility.Irakli Chitaia & Roland Omanadze - 2021 - Archive for Mathematical Logic 61 (1):19-31.
Hyperhypersimple sets and Q1 -reducibility.Irakli Chitaia - 2016 - Mathematical Logic Quarterly 62 (6):590-595.
Some properties of r-maximal sets and Q 1,N -reducibility.R. Sh Omanadze - 2015 - Archive for Mathematical Logic 54 (7-8):941-959.
Some properties of maximal sets.Roland S. H. Omanadze & Irakli O. Chitaia - 2015 - Logic Journal of the IGPL 23 (4):628-639.

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References found in this work

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 Iii & Paul H. Morris - 1974 - Journal of Symbolic Logic 39 (4):669 - 677.
On subcreative sets and S-reducibility.John T. Gill & Paul H. Morris - 1974 - Journal of Symbolic Logic 39 (4):669-677.

View all 8 references / Add more references