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The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

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Algebra and Logic Aims and scope

Computable categoricity in the Ershov hierarchy is studied. We consider F a -categorical 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 Ga-categorical structures.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. A. Bazhenov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    N. A. Bazhenov

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  1. N. A. Bazhenov
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Correspondence to N. A. Bazhenov.

Additional information

Supported by RFBR (project No. 14-01-00376), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-860.2014.1), and by the Russian Ministry of Education and Science (gov. contract No. 2014/139).

Translated from Algebra i Logika, Vol. 54, No. 2, pp. 137–157,March-April, 2015.

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Bazhenov, N.A. The Branching Theorem and Computable Categoricity in the Ershov Hierarchy. Algebra Logic 54, 91–104 (2015). https://doi.org/10.1007/s10469-015-9329-6

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  • DOI: https://doi.org/10.1007/s10469-015-9329-6

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