4 found
  1.  21
    Q1-degrees of c.e. sets.R. Sh Omanadze & Irakli O. Chitaia - 2012 - Archive for Mathematical Logic 51 (5-6):503-515.
    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} (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   9 citations  
  2.  17
    Some properties of maximal sets.Roland S. H. Omanadze & Irakli O. Chitaia - 2015 - Logic Journal of the IGPL 23 (4):628-639.
    Direct download (3 more)  
    Export citation  
    Bookmark   2 citations  
  3.  20
    Immunity properties and strong positive reducibilities.Irakli O. Chitaia, Roland Sh Omanadze & Andrea Sorbi - 2011 - Archive for Mathematical Logic 50 (3-4):341-352.
    We use certain strong Q-reducibilities, and their corresponding strong positive reducibilities, to characterize the hyperimmune sets and the hyperhyperimmune sets: if A is any infinite set then A is hyperimmune (respectively, hyperhyperimmune) if and only if for every infinite subset B of A, one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\rm ss} B}$$\end{document} (respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\overline{\rm s}} B}$$\end{document}): here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   1 citation  
  4.  4
    r‐Maximal sets and Q1,N‐reducibility.Roland Sh Omanadze & Irakli O. Chitaia - 2021 - Mathematical Logic Quarterly 67 (2):138-148.
    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.
    No categories
    Direct download (2 more)  
    Export citation