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On Δ 2 0 -categoricity of equivalence relations

Rod Downey, Alexander G. Melnikov & Keng Meng Ng

Annals of Pure and Applied Logic 166 (9):851-880 (2015)

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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.details 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 (...) Download Export citation Bookmark 3 citations
Generalization of Shapiro’s theorem to higher arities and noninjective notations.Dariusz Kalociński & Michał Wrocławski - 2022 - Archive for Mathematical Logic 62 (1):257-288.details In the framework of Stewart Shapiro, computations are performed directly on strings of symbols (numerals) whose abstract numerical interpretation is determined by a notation. Shapiro showed that a total unary function (unary relation) on natural numbers is computable in every injective notation if and only if it is almost constant or almost identity function (finite or co-finite set). We obtain a syntactic generalization of this theorem, in terms of quantifier-free definability, for functions and relations relatively intrinsically computable on certain types (...) Download Export citation Bookmark
Abelian p-groups and the Halting problem.Rodney Downey, Alexander G. Melnikov & Keng Meng Ng - 2016 - Annals of Pure and Applied Logic 167 (11):1123-1138.details Download Export citation Bookmark 3 citations
A Friedberg enumeration of equivalence structures.Rodney G. Downey, Alexander G. Melnikov & Keng Meng Ng - 2017 - Journal of Mathematical Logic 17 (2):1750008.details We solve a problem posed by Goncharov and Knight 639–681, 757]). More specifically, we produce an effective Friedberg enumeration of computable equivalence structures, up to isomorphism. We also prove that there exists an effective Friedberg enumeration of all isomorphism types of infinite computable equivalence structures. Download Export citation Bookmark 2 citations

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