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Algebra i logika, 2024, Volume 63, Number 3, Pages 235–247
DOI: https://doi.org/10.33048/alglog.2024.63.301 (Mi al2804) 		 
Decidable models of Ehrenfeucht theories

P. E. Alaevab, E. I. Khlestovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.33048/alglog.2024.63.301
Abstract: We study countable models of Ehrenfeucht theories, i.e., complete theories with a finite number of countable models, strictly larger than 1. The notion of a primely generated model is introduced. It is proved that if all complete types of an Ehrenfeucht theory have arithmetic complexity, then any of the primely generated models of the theory possesses an arithmetically complex isomorphic presentation.
Keywords: Ehrenfeucht theory, countable model, computable structure, decidable structure, arithmetic structure, arithmetic type.
Funding agency Grant number
Russian Science Foundation 23-11-00170
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0011
E. I. Khlestova is supported by Russian Science Foundation (project No. 23-11-00170).
Received: 21.02.2024
Revised: 11.04.2025
English version:
Algebra and Logic, 2024, Volume 63, Issue 3, Pages 155–163
DOI: https://doi.org/10.1007/s10469-025-09779-0
Document Type: Article
Language: Russian
Citation: P. E. Alaev, E. I. Khlestova, “Decidable models of Ehrenfeucht theories”, Algebra Logika, 63:3 (2024), 235–247; Algebra and Logic, 63:3 (2024), 155–163
Citation in format AMSBIB
\Bibitem{AlaKhl24}
\by P.~E.~Alaev, E.~I.~Khlestova
\paper Decidable models of Ehrenfeucht theories
\jour Algebra Logika
\yr 2024
\vol 63
\issue 3
\pages 235--247
\mathnet{http://mi.mathnet.ru/al2804}
\transl
\jour Algebra and Logic
\yr 2024
\vol 63
\issue 3
\pages 155--163
\crossref{https://doi.org/10.1007/s10469-025-09779-0}
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