Autostability of boolean algebras with distinguished ideal

Kogabaev, N. T.

doi:10.1007/bf02672914

Cited by 6 publications

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“…Note that B and C are countably categorical. Moreover, results in [6,7] imply that B and C are computably categorical. Fix a natural number m 0 such that…”

Section: Of Finite Binary Trees and Mapsmentioning

confidence: 94%

Complexity of some natural problems on the class of computable I-algebras

Kogabaev

2006

Sib Math J

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“…Note that B and C are countably categorical. Moreover, results in [6,7] imply that B and C are computably categorical. Fix a natural number m 0 such that…”

Section: Of Finite Binary Trees and Mapsmentioning

confidence: 94%

Complexity of some natural problems on the class of computable I-algebras

Kogabaev

2006

Sib Math J

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“…The branching theorem is widely used in research on computably categorical structures of various natural classes such as linear orders, Boolean algebras [13], Abelian p-groups [14,16], atomic ideal enrichments of Boolean algebras [15,17,18], etc. The theorem on unbounded structures has been applied in studying Abelian groups of infinite rank [14], projective planes [19,20], Boolean algebras with distinguished automorphism, etc.…”

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confidence: 99%

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

Bazhenov

2015

Algebra Logic

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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 G a -categorical structures.Research on computable categoricity of structures was initiated by B. L. van der Waerden who studied the question whether there exists an effective algorithm for constructing an isomorphism between two different algebraic closures of a field built in different ways. Subsequently, starting with 1950s, computable categoricity of structures was explored by A. I. Mal'tsev, A. Fröhlich, J. Shepherdson, S. S. Goncharov, J. Remmel, C. Ash, J. Knight, and many other authors.In investigating computably categorical structures, one of the most important problems is to gain an insight into computable categoricity relative to classes of known hierarchies of sets. In particular, of special interest is the Ershov hierarchy introduced in [1-3]. There are quite many works dealing with the Ershov hierarchy. (Among these, it is worth mentioning resent papers [4-10] that focus primarily on numberings in the Ershov hierarchy.) Research on computable categoricity relative to levels of the Ershov hierarchy was started in [11]. There, for an arbitrary a, which is *

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Computably categorical Boolean algebras enriched by ideals and atoms

Alaev

2012

Annals of Pure and Applied Logic

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Autostability of boolean algebras with distinguished ideal

Cited by 6 publications

References 2 publications

Complexity of some natural problems on the class of computable I-algebras

Complexity of some natural problems on the class of computable I-algebras

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

Computably categorical Boolean algebras enriched by ideals and atoms

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