4 found
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  1.  3
    On Isomorphism Classes of Computably Enumerable Equivalence Relations.Uri Andrews & Serikzhan A. Badaev - forthcoming - Journal of Symbolic Logic:1-26.
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  2.  35
    A Decomposition of the Rogers Semilattice of a Family of D.C.E. Sets.Serikzhan A. Badaev & Steffen Lempp - 2009 - Journal of Symbolic Logic 74 (2):618-640.
    Khutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. sets, has (up (...)
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  3.  23
    Rogers Semilattices of Families of Two Embedded Sets in the Ershov Hierarchy.Serikzhan A. Badaev, Mustafa Manat & Andrea Sorbi - 2012 - Mathematical Logic Quarterly 58 (4-5):366-376.
    Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a sufficient condition on a, so that for every equation image-computable family of two embedded sets, i.e., two sets A, B, with A properly contained in B, the Rogers semilattice of the family is infinite. This condition is satisfied by every notation of ω; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satisfies this condition. On the (...)
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  4.  8
    Friedberg Numberings in the Ershov Hierarchy.Serikzhan A. Badaev, Mustafa Manat & Andrea Sorbi - 2015 - Archive for Mathematical Logic 54 (1-2):59-73.