Algebra and Logic

, Volume 54, Issue 2, pp 91–104 | Cite as

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

Article

Computable categoricity in the Ershov hierarchy is studied. We consider Fa-categorical and Ga-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 Fa-categorical structures. As a consequence we obtain a description of Fa-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.

Keywords

computable categoricity Ershov hierarchy Fa-categoricity Ga-categoricity branching structure 

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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