Browsing by Author "Faizrahmanov M."

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  • Complements for enumeration Π1 0-degrees 
    Faizrahmanov M. (2013)
    We consider the question of the existence of complements for the enumeration degrees of cocomputably enumerable sets in the local structure of e-degrees. © 2013 Pleiades Publishing, Ltd.
  • Computable numberings of families of low sets and Turing jumps in the Ershov hierarchy 
    Faizrahmanov M. (2010)
    If ν and μ are some Δcomputable numberings of families of sets of the naturals then P(x,y) ⇔ ν(x)′ ≠ μ(y) is a Σpredicate. Deriving corollaries from this result, we obtain a sufficient condition for existence of a Δcomputable ...
  • Jump inversions of algebraic structures and Σ-definability 
    Faizrahmanov M.; Kach A.; Kalimullin I.; Montalbán A.; Puzarenko V. (2019)
    © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim It is proved that for every countable structure A and a computable successor ordinal α there is a countable structure A−α which is (Formula presented.) -least among all ...
  • Limitwise monotonic sets of reals 
    Faizrahmanov M.; Kalimullin I. (2015)
    © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. We extend the limitwise monotonicity notion to the case of arbitrary computable linear ordering to get a set which is limitwise monotonic precisely in the non-computable ...
  • Limitwise Monotonic Spectra and Their Generalizations 
    Faizrahmanov M. (2021)
    The current work studies the limitwise monotonic spectra introduced by Downey, Kach and Turetsky [6]. In the first part of the paper, we study the limitwise monotonic spectra of subsets and sequences of subsets of N. In ...
  • Maximality and minimality under limitwise monotonic reducibility 
    Faizrahmanov M.; Kalimullin I.; Zainetdinov D. (2014)
    © 2014, Pleiades Publishing, Ltd. In the paper we study the maximal and minimal objects under Σ-reducibility of the families of the form {ℕ ↾ n: n ∈ A}.
  • Minimal generalized computable enumerations and high degrees 
    Faizrahmanov M. (2017)
    © 2017, Pleiades Publishing, Ltd. We establish that the set of minimal generalized computable enumerations of every infinite family computable with respect to a high oracle is effectively infinite. We find some sufficient ...
  • On arithmetical level of the class of superhigh sets 
    Faizrahmanov M. (2014)
    We determine the proper arithmetical level of the class of superhigh sets. © 2014 Allerton Press, Inc.
  • Partial Decidable Presentations in Hyperarithmetic 
    Kalimullin I.; Puzarenko V.; Faizrahmanov M. (2019)
    © 2019, Pleiades Publishing, Inc. We study the problem of the existence of decidable and positive Π11- and Σ11-numberings of the families of Π11- and Σ11-cones with respect to inclusion. Some laws are found that reflect ...
  • Positive Presentations of Families Relative to e-Oracles 
    Kalimullin I.; Puzarenko V.; Faizrahmanov M. (2018)
    © 2018, Pleiades Publishing, Ltd. We introduce the notion of A-numbering which generalizes the classical notion of numbering. All main attributes of classical numberings are carried over to the objects considered here. The ...
  • The enumeration spectrum hierarchy of n-families 
    Faizrahmanov M.; Kalimullin I. (2016)
    © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWe introduce a hierarchy of sets which can be derived from the integers using countable collections. Such families can be coded into countable algebraic structures preserving ...
  • The enumeration spectrum hierarchy of α-families and low<inf>α</inf> degrees 
    Faizrahmanov M.; Kalimullin I. (2016)
    © J.UCS.In this paper we introduce a hierarchy of families which can be derived from the integers using countable collections. This hierarchy coincides with the von Neumann hierarchy of hereditary countable sets in the ...
  • The least Σ-jump inversion theorem for N-families 
    Faizrahmanov M.; Kalimullin I.; Montalbán A.; Puzarenko V. (2017)
    © J.UCS. Studying the Σ-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set X ≥ T ∅׳_there is a family of sets F which is the Σ-least countable family whose Σ-jump is Σ-equivalent ...
  • Turing and enumeration jumps in the Ershov hierarchy 
    Faizrahmanov M.; Kalimullin I. (2012)
    In the article, we study the behaviour of enumeration jumps of sets of low e-degrees in the Ershov hierarchy. © 2010 The Author. Published by Oxford University Press. All rights reserved.

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