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Decidable Categoricity Spectra for Almost Prime Models. / Bazhenov, N. A.; Marchuk, M. I.

In: Algebra and Logic, Vol. 62, No. 4, 09.2024, p. 291-302.

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

Harvard

Bazhenov, NA & Marchuk, MI 2024, 'Decidable Categoricity Spectra for Almost Prime Models', Algebra and Logic, vol. 62, no. 4, pp. 291-302. https://doi.org/10.1007/s10469-024-09746-1

APA

Bazhenov, N. A., & Marchuk, M. I. (2024). Decidable Categoricity Spectra for Almost Prime Models. Algebra and Logic, 62(4), 291-302. https://doi.org/10.1007/s10469-024-09746-1

Vancouver

Bazhenov NA, Marchuk MI. Decidable Categoricity Spectra for Almost Prime Models. Algebra and Logic. 2024 Sept;62(4):291-302. doi: 10.1007/s10469-024-09746-1

Author

Bazhenov, N. A. ; Marchuk, M. I. / Decidable Categoricity Spectra for Almost Prime Models. In: Algebra and Logic. 2024 ; Vol. 62, No. 4. pp. 291-302.

BibTeX

@article{fd2aa61e4f5246d4aeb586437ed26c88,
title = "Decidable Categoricity Spectra for Almost Prime Models",
abstract = "We study decidable categoricity spectra for almost prime models. For any computable collection {Di}i∈ω, where Di either is a c.e. set or Di = PA, we construct a sequence of almost prime models {Mi}i∈ω elementarily embedded in each other, in which case for any i there exists a finite collection of constants such that the model Mi in the expansion by these constants has degree of decidable categoricity degT (Di), if Di is a c.e. set, and has no degree of decidable categoricity if Di = PA. The result obtained extends that of S. S. Goncharov, V. Harizanov, and R. Miller [Sib. Adv. Math., 30, No. 3, 200-212 (2020)].",
keywords = "PA-degree, autostability relative to strong constructivizations, computable categoricity, computable model, decidable categoricity, decidable categoricity spectrum, decidable model, degree of decidable categoricity",
author = "Bazhenov, {N. A.} and Marchuk, {M. I.}",
note = "N. A. Bazhenov and M. I. Marchuk are supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 075-15-2022-282.",
year = "2024",
month = sep,
doi = "10.1007/s10469-024-09746-1",
language = "English",
volume = "62",
pages = "291--302",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "4",

}

RIS

TY - JOUR

T1 - Decidable Categoricity Spectra for Almost Prime Models

AU - Bazhenov, N. A.

AU - Marchuk, M. I.

N1 - N. A. Bazhenov and M. I. Marchuk are supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 075-15-2022-282.

PY - 2024/9

Y1 - 2024/9

N2 - We study decidable categoricity spectra for almost prime models. For any computable collection {Di}i∈ω, where Di either is a c.e. set or Di = PA, we construct a sequence of almost prime models {Mi}i∈ω elementarily embedded in each other, in which case for any i there exists a finite collection of constants such that the model Mi in the expansion by these constants has degree of decidable categoricity degT (Di), if Di is a c.e. set, and has no degree of decidable categoricity if Di = PA. The result obtained extends that of S. S. Goncharov, V. Harizanov, and R. Miller [Sib. Adv. Math., 30, No. 3, 200-212 (2020)].

AB - We study decidable categoricity spectra for almost prime models. For any computable collection {Di}i∈ω, where Di either is a c.e. set or Di = PA, we construct a sequence of almost prime models {Mi}i∈ω elementarily embedded in each other, in which case for any i there exists a finite collection of constants such that the model Mi in the expansion by these constants has degree of decidable categoricity degT (Di), if Di is a c.e. set, and has no degree of decidable categoricity if Di = PA. The result obtained extends that of S. S. Goncharov, V. Harizanov, and R. Miller [Sib. Adv. Math., 30, No. 3, 200-212 (2020)].

KW - PA-degree

KW - autostability relative to strong constructivizations

KW - computable categoricity

KW - computable model

KW - decidable categoricity

KW - decidable categoricity spectrum

KW - decidable model

KW - degree of decidable categoricity

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200042399&origin=inward&txGid=aa8b64030957ed697d90c1b370ffafda

UR - https://www.mendeley.com/catalogue/27240cb3-8acd-30b2-a8b4-97136e145171/

U2 - 10.1007/s10469-024-09746-1

DO - 10.1007/s10469-024-09746-1

M3 - Article

VL - 62

SP - 291

EP - 302

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 4

ER -

ID: 60410698