Degrees of Autostability for Prime Boolean Algebras

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Degrees of Autostability for Prime Boolean Algebras. / Bazhenov, N. A.; Marchuk, M. I.

In: Algebra and Logic, Vol. 57, No. 2, 01.06.2018, p. 98-114.

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

Harvard

Bazhenov, NA & Marchuk, MI 2018, 'Degrees of Autostability for Prime Boolean Algebras', Algebra and Logic, vol. 57, no. 2, pp. 98-114. https://doi.org/10.1007/s10469-018-9483-8

APA

Bazhenov, N. A., & Marchuk, M. I. (2018). Degrees of Autostability for Prime Boolean Algebras. Algebra and Logic, 57(2), 98-114. https://doi.org/10.1007/s10469-018-9483-8

Vancouver

Bazhenov NA, Marchuk MI. Degrees of Autostability for Prime Boolean Algebras. Algebra and Logic. 2018 Jun 1;57(2):98-114. doi: 10.1007/s10469-018-9483-8

Author

Bazhenov, N. A. ; Marchuk, M. I. / Degrees of Autostability for Prime Boolean Algebras. In: Algebra and Logic. 2018 ; Vol. 57, No. 2. pp. 98-114.

BibTeX

@article{55f4ba56f7db469eaa91d352e7147317,

title = "Degrees of Autostability for Prime Boolean Algebras",

abstract = "We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.",

keywords = "autostability, autostability relative to strong constructivizations, autostability spectrum, Boolean algebra, categoricity spectrum, computable categoricity, computable model, decidable model, degree of autostability, degree of categoricity, prime model, FIELDS, COMPUTABLE CATEGORICITY, STRONG CONSTRUCTIVIZATIONS",

author = "Bazhenov, {N. A.} and Marchuk, {M. I.}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s10469-018-9483-8",

language = "English",

volume = "57",

pages = "98--114",

journal = "Algebra and Logic",

issn = "0002-5232",

publisher = "Springer US",

number = "2",

}

RIS

TY - JOUR

T1 - Degrees of Autostability for Prime Boolean Algebras

AU - Bazhenov, N. A.

AU - Marchuk, M. I.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.

AB - We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.

KW - autostability

KW - autostability relative to strong constructivizations

KW - autostability spectrum

KW - Boolean algebra

KW - categoricity spectrum

KW - computable categoricity

KW - computable model

KW - decidable model

KW - degree of autostability

KW - degree of categoricity

KW - prime model

KW - FIELDS

KW - COMPUTABLE CATEGORICITY

KW - STRONG CONSTRUCTIVIZATIONS

UR - http://www.scopus.com/inward/record.url?scp=85050685818&partnerID=8YFLogxK

U2 - 10.1007/s10469-018-9483-8

DO - 10.1007/s10469-018-9483-8

M3 - Article

AN - SCOPUS:85050685818

VL - 57

SP - 98

EP - 114

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 2

ER -

ID: 15966852