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Iskander Kalimullin [7]Iskander Sh Kalimullin [4]Iskander S. Kalimullin [1]
  1.  13
    Categoricity Spectra for Rigid Structures.Ekaterina Fokina, Andrey Frolov & Iskander Kalimullin - 2016 - Notre Dame Journal of Formal Logic 57 (1):45-57.
    For a computable structure $\mathcal {M}$, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of $\mathcal {M}$. If the spectrum has a least degree, this degree is called the degree of categoricity of $\mathcal {M}$. In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.
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  2.  47
    Degrees of Categoricity of Computable Structures.Ekaterina B. Fokina, Iskander Kalimullin & Russell Miller - 2010 - Archive for Mathematical Logic 49 (1):51-67.
    Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).
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  3.  6
    Jump Inversions of Algebraic Structures and Σ‐Definability.Marat Faizrahmanov, Asher Kach, Iskander Kalimullin, Antonio Montalbán & Vadim Puzarenko - 2019 - Mathematical Logic Quarterly 65 (1):37-45.
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  4.  15
    Degrees of Categoricity and Spectral Dimension.Nikolay A. Bazhenov, Iskander Sh Kalimullin & Mars M. Yamaleev - 2018 - Journal of Symbolic Logic 83 (1):103-116.
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  5.  20
    Degree Spectra and Immunity Properties.Barbara F. Csima & Iskander S. Kalimullin - 2010 - Mathematical Logic Quarterly 56 (1):67-77.
    We analyze the degree spectra of structures in which different types of immunity conditions are encoded. In particular, we give an example of a structure whose degree spectrum coincides with the hyperimmune degrees. As a corollary, this shows the existence of an almost computable structure of which the complement of the degree spectrum is uncountable.
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  6.  29
    Density Results in the Δ 2 0 E-Degrees.Marat M. Arslanov, Iskander Sh Kalimullin & Andrea Sorbi - 2001 - Archive for Mathematical Logic 40 (8):597-614.
    We show that the Δ0 2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.
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  7.  15
    Foundations of Online Structure Theory.Nikolay Bazhenov, Rod Downey, Iskander Kalimullin & Alexander Melnikov - 2019 - Bulletin of Symbolic Logic 25 (2):141-181.
    The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.
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  8.  14
    Automatic and Polynomial-Time Algebraic Structures.Nikolay Bazhenov, Matthew Harrison-Trainor, Iskander Kalimullin, Alexander Melnikov & Keng Meng Ng - 2019 - Journal of Symbolic Logic 84 (4):1630-1669.
    A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma (...)
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  9.  2
    On Downey's Conjecture.Marat M. Arslanov, Iskander Sh Kalimullin & Steffen Lempp - 2010 - Journal of Symbolic Logic 75 (2):401-441.
    We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.
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  10.  2
    Limitwise Monotonic Sets of Reals.Marat Faizrahmanov & Iskander Kalimullin - 2015 - Mathematical Logic Quarterly 61 (3):224-229.
  11. The Enumeration Spectrum Hierarchy Ofn-Families.Marat Faizrahmanov & Iskander Kalimullin - 2016 - Mathematical Logic Quarterly 62 (4-5):420-426.
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