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Algebra Logika, 2004, Volume 43, Number 3, Pages 321–340 (Mi al72)  

This article is cited in 1 scientific paper (total in 1 paper)

Elementary Pairs of Primitive Normal Theories

E. A. Palyutin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The main objective of the paper is proving that classes of primitive normal, primitive bound, antiadditive, and additive theories are closed under $P$-expansions. This phenomenon is quite remarkable, for the main “structure” classes of theories studied within model theory (such as stable, totally transcendental, etc.) do not possess such a property. Furthermore, it is proved that primitive bound theories are $P$-stable, and we furnish an example of a primitive bound theory with models that are not primitive bound.

Keywords: elementary pairs, primitive normal theory, primitive bound theory, antiadditive theory, additive theory, primitive bound model

Full text: PDF file (223 kB)
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English version:
Algebra and Logic, 2004, 43:3, 179–189

Bibliographic databases:

UDC: 510.67:512.57
Received: 19.12.2002

Citation: E. A. Palyutin, “Elementary Pairs of Primitive Normal Theories”, Algebra Logika, 43:3 (2004), 321–340; Algebra and Logic, 43:3 (2004), 179–189

Citation in format AMSBIB
\Bibitem{Pal04}
\by E.~A.~Palyutin
\paper Elementary Pairs of Primitive Normal Theories
\jour Algebra Logika
\yr 2004
\vol 43
\issue 3
\pages 321--340
\mathnet{http://mi.mathnet.ru/al72}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2084039}
\zmath{https://zbmath.org/?q=an:1115.03029}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 3
\pages 179--189
\crossref{https://doi.org/10.1023/B:ALLO.0000028931.44811.f1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249093690}


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    This publication is cited in the following articles:
    1. Yeshkeyev A.R., Kassymetova M.T., Ulbrikht O.I., “Criterion For the Cosemanticness of the Abelian Groups in the Enriched Signature”, Bull. Karaganda Univ-Math., 89:1 (2018), 49–60  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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