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Algebra Logika, 2015, Volume 54, Number 2, Pages 137–157 (Mi al684)  

The branching theorem and computable categoricity in the Ershov hierarchy

N. A. Bazhenovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: Computable categoricity in the Ershov hierarchy is studied. We consider $F_a$- and $G_a$-categorical structures. These were introduced by B. Khoussainov, F. Stephan, and Y. Yang for $a$, which is a notation for a constructive ordinal. A generalization of the branching theorem is proved for $F_a$-categorical structures. As a consequence we obtain a description of $F_a$-categorical structures for classes of Boolean algebras and Abelian $p$-groups. Furthermore, it is shown that the branching theorem cannot be generalized to $G_a$-categorical structures.

Keywords: computable categoricity, Ershov hierarchy, $F_a$-categoricity, $G_a$-categoricity, branching structure.

DOI: https://doi.org/10.17377/alglog.2015.54.201

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English version:
Algebra and Logic, 2015, 54:2, 91–104

Bibliographic databases:

UDC: 510.5
Received: 04.11.2013
Revised: 06.02.2015

Citation: N. A. Bazhenov, “The branching theorem and computable categoricity in the Ershov hierarchy”, Algebra Logika, 54:2 (2015), 137–157; Algebra and Logic, 54:2 (2015), 91–104

Citation in format AMSBIB
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