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  1. A computably categorical structure whose expansion by a constant has infinite computable dimension.Denis Hirschfeldt, Bakhadyr Khoussainov & Richard Shore - 2003 - Journal of Symbolic Logic 68 (4):1199-1241.
    Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.
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  • Degree spectra of relations on computable structures.Denis R. Hirschfeldt - 2000 - Bulletin of Symbolic Logic 6 (2):197-212.
    There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. Several different notions of effectiveness of model-theoretic structures have been investigated. This communication is concerned withcomputablestructures, that is, structures with computable domains whose constants, functions, and relations are uniformly computable.In model theory, we identify isomorphic structures. (...)
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  • Non-density in punctual computability.Noam Greenberg, Matthew Harrison-Trainor, Alexander Melnikov & Dan Turetsky - 2021 - Annals of Pure and Applied Logic 172 (9):102985.
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  • Degrees of orders on torsion-free Abelian groups.Asher M. Kach, Karen Lange & Reed Solomon - 2013 - Annals of Pure and Applied Logic 164 (7-8):822-836.
    We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree.
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  • Degree spectra of relations on structures of finite computable dimension.Denis R. Hirschfeldt - 2002 - Annals of Pure and Applied Logic 115 (1-3):233-277.
    We show that for every computably enumerable degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is { 0 , a } , thus answering a question of Goncharov and Khoussainov 55–57). We also show that this theorem remains true with α -c.e. in place of c.e. for any α∈ω∪{ω} . A modification of the proof of this result similar to what was done in Hirschfeldt (...)
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  • $\Pi _{1}^{0}$ Classes and Strong Degree Spectra of Relations.John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denis R. Hirschfeldt, Carl G. Jockusch, Timothy McNicholl & Sarah Pingrey - 2007 - Journal of Symbolic Logic 72 (3):1003 - 1018.
    We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.
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  • A computably stable structure with no Scott family of finitary formulas.Peter Cholak, Richard A. Shore & Reed Solomon - 2006 - Archive for Mathematical Logic 45 (5):519-538.
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