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Degrees of categoricity of computable structures
Archive for Mathematical Logic 49 (1):51-67 (2010)
Abstract
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)Author's Profile
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Citations of this work
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.
A computable functor from graphs to fields.Russell Miller, Bjorn Poonen, Hans Schoutens & Alexandra Shlapentokh - 2018 - Journal of Symbolic Logic 83 (1):326-348.
Degrees That Are Not Degrees of Categoricity.Bernard Anderson & Barbara Csima - 2016 - Notre Dame Journal of Formal Logic 57 (3):389-398.
Categoricity Spectra for Rigid Structures.Ekaterina Fokina, Andrey Frolov & Iskander Kalimullin - 2016 - Notre Dame Journal of Formal Logic 57 (1):45-57.
Degrees of categoricity and spectral dimension.Nikolay A. Bazhenov, Iskander Sh Kalimullin & Mars M. Yamaleev - 2018 - Journal of Symbolic Logic 83 (1):103-116.
References found in this work
Degree spectra and computable dimensions in algebraic structures.Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko - 2002 - Annals of Pure and Applied Logic 115 (1-3):71-113.
Enumerations in computable structure theory.Sergey Goncharov, Valentina Harizanov, Julia Knight, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Annals of Pure and Applied Logic 136 (3):219-246.
Computably categorical structures and expansions by constants.Peter Cholak, Sergey Goncharov, Bakhadyr Khoussainov & Richard A. Shore - 1999 - Journal of Symbolic Logic 64 (1):13-37.
Number theoretic concepts and recursive well-orderings.G. Kreisel, J. Shoenfield & Hao Wang - 1960 - Archive for Mathematical Logic 5 (1-2):42-64.
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