4 found
  1.  18
    Q 1-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 Q 1-degrees linearly ordered under ${\leq_{Q_1}}$ with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q 1-degrees are not an upper semilattice. The main result of this paper is that the Q 1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for ${\Pi_1^0}$ s 1-degrees.
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  2.  11
    Some Properties of Maximal Sets.Roland S. H. Omanadze & Irakli O. Chitaia - 2015 - Logic Journal of the IGPL 23 (4):628-639.
  3.  15
    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 ${\overline{K}\not\le_{\rm ss} B}$ (respectively, ${\overline{K}\not\le_{\overline{\rm s}} B}$ ): here ${\le_{\overline{\rm s}}}$ is the finite-branch version of s-reducibility, ≤ss is the computably bounded version of ${\le_{\overline{\rm s}}}$ , and ${\overline{K}}$ is the complement of the halting set. (...)
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  4. R ‐Maximal Sets and Q1,N‐Reducibility.Roland Sh Omanadze & Irakli O. Chitaia - forthcoming - Mathematical Logic Quarterly.
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