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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 719–727 (Mi semr948)  

Mathematical logic, algebra and number theory

Finding $2^{\aleph_0}$ countable models for ordered theories

B. Baizhanova, J. T. Baldwinb, T. Zambarnayaca

a Institute of Mathematics and Mathematical Modeling, 125 Pushkin St., 050010, Almaty, Kazakhstan
b University of Illinois at Chicago, 1200 West Harrison St., 60607, Chicago, Illinois
c Al-Farabi Kazakh National University, 71 al-Farabi Ave., 050040, Almaty, Kazakhstan

Abstract: The article is focused on finding conditions that imply small theories of linear order have the maximum number of countable non-isomorphic models. We introduce the notion of extreme triviality of non-principal types, and prove that a theory of order, which has such a type, has $2^{\aleph_0}$ countable non-isomorphic models.

Keywords: countable model, linear order, omitting types.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan AP05134992
The work is financially supported by the Ministry of Education and Science of the Republic of Kazakhstan (grant AP05134992).


DOI: https://doi.org/10.17377/semi.2018.15.057

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Bibliographic databases:

Document Type: Article
UDC: 510.67
MSC: 03C15, 03C64
Received May 11, 2018, published June 14, 2018
Language: English

Citation: B. Baizhanov, J. T. Baldwin, T. Zambarnaya, “Finding $2^{\aleph_0}$ countable models for ordered theories”, Sib. Èlektron. Mat. Izv., 15 (2018), 719–727

Citation in format AMSBIB
\Bibitem{BaiBalZam18}
\by B.~Baizhanov, J.~T.~Baldwin, T.~Zambarnaya
\paper Finding $2^{\aleph_0}$ countable models for ordered theories
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 719--727
\mathnet{http://mi.mathnet.ru/semr948}
\crossref{https://doi.org/10.17377/semi.2018.15.057}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200057}


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