Categoricity Spectra of Computable Structures

Standard

Categoricity Spectra of Computable Structures. / Bazhenov, N. A.

In: Journal of Mathematical Sciences (United States), Vol. 256, No. 1, 07.2021, p. 34-50.

Research output: Contribution to journal › Article › peer-review

Harvard

Bazhenov, NA 2021, 'Categoricity Spectra of Computable Structures', Journal of Mathematical Sciences (United States), vol. 256, no. 1, pp. 34-50. https://doi.org/10.1007/s10958-021-05419-x

APA

Bazhenov, N. A. (2021). Categoricity Spectra of Computable Structures. Journal of Mathematical Sciences (United States), 256(1), 34-50. https://doi.org/10.1007/s10958-021-05419-x

Vancouver

Bazhenov NA. Categoricity Spectra of Computable Structures. Journal of Mathematical Sciences (United States). 2021 Jul;256(1):34-50. doi: 10.1007/s10958-021-05419-x

Author

Bazhenov, N. A. / Categoricity Spectra of Computable Structures. In: Journal of Mathematical Sciences (United States). 2021 ; Vol. 256, No. 1. pp. 34-50.

BibTeX

@article{1efb9b1140d748c4a4d33bf520525a06,

title = "Categoricity Spectra of Computable Structures",

abstract = "The categoricity spectrum of a computable structure S is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of S. The degree of categoricity of S is the least degree in the categoricity spectrum of S. This paper is a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We construct a new series of examples of degrees of categoricity for linear orders.",

keywords = "03C57, 03D45, autostability, autostability relative to strong constructivizations, Boolean algebra, categoricity spectrum, computable categoricity, computable structure, decidable categoricity, degree of categoricity, index set, linear order",

author = "Bazhenov, {N. A.}",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2021",

month = jul,

doi = "10.1007/s10958-021-05419-x",

language = "English",

volume = "256",

pages = "34--50",

journal = "Journal of Mathematical Sciences (United States)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Categoricity Spectra of Computable Structures

AU - Bazhenov, N. A.

PY - 2021/7

Y1 - 2021/7

N2 - The categoricity spectrum of a computable structure S is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of S. The degree of categoricity of S is the least degree in the categoricity spectrum of S. This paper is a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We construct a new series of examples of degrees of categoricity for linear orders.

AB - The categoricity spectrum of a computable structure S is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of S. The degree of categoricity of S is the least degree in the categoricity spectrum of S. This paper is a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We construct a new series of examples of degrees of categoricity for linear orders.

KW - 03C57

KW - 03D45

KW - autostability

KW - autostability relative to strong constructivizations

KW - Boolean algebra

KW - categoricity spectrum

KW - computable categoricity

KW - computable structure

KW - decidable categoricity

KW - degree of categoricity

KW - index set

KW - linear order

UR - http://www.scopus.com/inward/record.url?scp=85106673672&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05419-x

DO - 10.1007/s10958-021-05419-x

M3 - Article

AN - SCOPUS:85106673672

VL - 256

SP - 34

EP - 50

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 1

ER -

ID: 34030211