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  1. $$sQ_1$$-degrees of computably enumerable sets.Roland Sh Omanadze - forthcoming - Archive for Mathematical Logic:1-17.
    We show that the sQ-degree of a hypersimple set includes an infinite collection of $$sQ_1$$ -degrees linearly ordered under $$\le _{sQ_1}$$ with order type of the integers and each c.e. set in these sQ-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the $$sQ_1$$ -reducibility ordering. We show that the c.e. $$sQ_1$$ -degrees are not dense and if a is a c.e. $$sQ_1$$ -degree such that $$o_{sQ_1}<_{sQ_1}a<_{sQ_1}o'_{sQ_1}$$, then there exist (...)
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  • $$sQ_1$$ s Q 1 -degrees of computably enumerable sets.Roland Sh Omanadze - forthcoming - Archive for Mathematical Logic:1-17.
    We show that the sQ-degree of a hypersimple set includes an infinite collection of \-degrees linearly ordered under \ with order type of the integers and each c.e. set in these sQ-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the \-reducibility ordering. We show that the c.e. \-degrees are not dense and if a is a c.e. \-degree such that \, then there exist infinitely many pairwise sQ-incomputable c.e. (...)
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  • r ‐Maximal sets and Q1,N‐reducibility.Roland Sh Omanadze & Irakli O. Chitaia - forthcoming - Mathematical Logic Quarterly.
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