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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

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.

UDC: 510.67

MSC: 03C15, 03C64

Received May 11, 2018, published June 14, 2018

Language: English

DOI: 10.17377/semi.2018.15.057



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