Noncomputability of classes of pappian and desarguesian projective planes

Kogabaev, N. T.

doi:10.1134/s0037446613020092

Sib Math J

2013

DOI: 10.1134/s0037446613020092

|View full text |Cite

Noncomputability of classes of pappian and desarguesian projective planes

N. T. Kogabaev

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

2018

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.…”

mentioning

confidence: 99%

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

Bazhenov

2015

Algebra Logic

View full text Add to dashboard Cite

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 *

show abstract

“…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.…”

mentioning

confidence: 99%

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

Bazhenov

2015

Algebra Logic

View full text Add to dashboard Cite

show abstract

The Theory of Projective Planes is Complete with Respect to Degree Spectra and Effective Dimensions

Kogabaev

2015

Algebra Logic

View full text Add to dashboard Cite

The Δ0 α -Computable Enumerations of the Classes of Projective Planes

Voĭtov

2018

Sib Math J

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Noncomputability of classes of pappian and desarguesian projective planes

Cited by 3 publications

References 3 publications

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

The Branching Theorem and Computable Categoricity in the Ershov Hierarchy

The Theory of Projective Planes is Complete with Respect to Degree Spectra and Effective Dimensions

The Δ0 α -Computable Enumerations of the Classes of Projective Planes

Contact Info

Product

Resources

About