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Andrey Frolov [3]Andrey N. Frolov [2]
  1.  36
    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.  24
    Increasing η ‐representable degrees.Andrey N. Frolov & Maxim V. Zubkov - 2009 - Mathematical Logic Quarterly 55 (6):633-636.
    In this paper we prove that any Δ30 degree has an increasing η -representation. Therefore, there is an increasing η -representable set without a strong η -representation.
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  3.  46
    Degree spectra of the successor relation of computable linear orderings.Jennifer Chubb, Andrey Frolov & Valentina Harizanov - 2009 - Archive for Mathematical Logic 48 (1):7-13.
    We establish that for every computably enumerable (c.e.) Turing degree b the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.
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  4.  13
    Computable linear orders and products.Andrey N. Frolov, Steffen Lempp, Keng Meng Ng & Guohua Wu - 2020 - Journal of Symbolic Logic 85 (2):605-623.
    We characterize the linear order types $\tau $ with the property that given any countable linear order $\mathcal {L}$, $\tau \cdot \mathcal {L}$ is a computable linear order iff $\mathcal {L}$ is a computable linear order, as exactly the finite nonempty order types.
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  5.  19
    The Simplest Low Linear Order with No Computable Copies.Andrey Frolov & Maxim Zubkov - 2024 - Journal of Symbolic Logic 89 (1):97-111.
    A low linear order with no computable copy constructed by C. Jockusch and R. Soare has Hausdorff rank equal to $2$. In this regard, the question arises, how simple can be a low linear order with no computable copy from the point of view of the linear order type? The main result of this work is an example of a low strong $\eta $ -representation with no computable copy that is the simplest possible example.
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