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Eurasian Math. J., 2018, Volume 9, Number 4, Pages 91–98 (Mi emj315)  

On commutativity of circularly ordered c-o-stable groups

V. V. Verbovskiy

Center of Mathematics and Cybernetics, The Kazakh-British Technical University, 59 Tole bi St, 050000, Almaty, Republic of Kazakhstan

Abstract: A circularly ordered structure is called c-o-stable in $\lambda$, if for any subset $A$ of cardinality at most $\lambda$ and for any cut $s$ there exist at most $\lambda$ one-types over $A$ that are consistent with $s$. A theory is called c-o-stable if there exists an infinite $\lambda$ such that all its models are c-o-stable in $\lambda$. In the paper, it is proved that any circularly ordered group, whose elementary theory is c-o-stable, is Abelian.

Keywords and phrases: circularly ordered group, o-minimality, commutative group, o-stability.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan AP05132688
This work was supported by the grant AP05132688 of the Ministry of Education and Science of the Republic of Kazakhstan.


DOI: https://doi.org/10.32523/2077-9879-2018-9-4-91-98

Full text: PDF file (363 kB)
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Bibliographic databases:

UDC: 03B10, 03C52, 03C60, 03C64
Received: 09.02.2017
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Citation: V. V. Verbovskiy, “On commutativity of circularly ordered c-o-stable groups”, Eurasian Math. J., 9:4 (2018), 91–98

Citation in format AMSBIB
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\paper On commutativity of circularly ordered c-o-stable groups
\jour Eurasian Math. J.
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\vol 9
\issue 4
\pages 91--98
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\crossref{https://doi.org/10.32523/2077-9879-2018-9-4-91-98}
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