Decidable Categoricity Spectra for Almost Prime Models. / Bazhenov, N. A.; Marchuk, M. I.
In: Algebra and Logic, Vol. 62, No. 4, 09.2023, p. 291-302.Research output: Contribution to journal › Article › peer-review
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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 - 2023/9
Y1 - 2023/9
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