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  1. Degrees of Categoricity of Trees and the Isomorphism Problem.Mohammad Assem Mahmoud - forthcoming - Mathematical Logic Quarterly.
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  • Degrees of Bi-Embeddable Categoricity of Equivalence Structures.Nikolay Bazhenov, Ekaterina Fokina, Dino Rossegger & Luca San Mauro - 2019 - Archive for Mathematical Logic 58 (5-6):543-563.
    We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain results (...)
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  • Degrees of Categoricity and the Hyperarithmetic Hierarchy.Barbara F. Csima, Johanna N. Y. Franklin & Richard A. Shore - 2013 - Notre Dame Journal of Formal Logic 54 (2):215-231.
    We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...)
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  • 2011 North American Annual Meeting of the Association for Symbolic Logic.Itay Neeman - 2012 - Bulletin of Symbolic Logic 18 (2):275-305.
  • Categoricity Spectra for Polymodal Algebras.Nikolay Bazhenov - 2016 - Studia Logica 104 (6):1083-1097.
    We investigate effective categoricity for polymodal algebras. We prove that the class of polymodal algebras is complete with respect to degree spectra of nontrivial structures, effective dimensions, expansion by constants, and degree spectra of relations. In particular, this implies that every categoricity spectrum is the categoricity spectrum of a polymodal algebra.
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  • Effective Algebraicity.Rebecca M. Steiner - 2013 - Archive for Mathematical Logic 52 (1-2):91-112.
    Results of R. Miller in 2009 proved several theorems about algebraic fields and computable categoricity. Also in 2009, A. Frolov, I. Kalimullin, and R. Miller proved some results about the degree spectrum of an algebraic field when viewed as a subfield of its algebraic closure. Here, we show that the same computable categoricity results also hold for finite-branching trees under the predecessor function and for connected, finite-valence, pointed graphs, and we show that the degree spectrum results do not hold for (...)
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  • 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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  • A Computable Functor From Graphs to Fields.Russell Miller, Bjorn Poonen, Hans Schoutens & Alexandra Shlapentokh - 2018 - Journal of Symbolic Logic 83 (1):326-348.
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  • Degrees of Categoricity on a Cone Via Η-Systems.Barbara F. Csima & Matthew Harrison-Trainor - 2017 - Journal of Symbolic Logic 82 (1):325-346.
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