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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.
Received May 11, 2018, published June 14, 2018
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
Linking options:
https://www.mathnet.ru/eng/semr948 https://www.mathnet.ru/eng/semr/v15/p719
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Abstract page: | 191 | Full-text PDF : | 57 | References: | 23 |
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