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LOCALLY O-MINIMAL STRUCTURES WITH TAME TOPOLOGICAL PROPERTIES

Part of: Model theory

Published online by Cambridge University Press:  08 October 2021

MASATO FUJITA Open the ORCID record for MASATO FUJITA [Opens in a new window]
MASATO FUJITA*
Affiliation:
DEPARTMENT OF LIBERAL ARTS JAPAN COAST GUARD ACADEMY 5-1 WAKABA-CHO, KURE HIROSHIMA 737-8512, JAPAN
*
E-mail: fujita.masato.p34@kyoto-u.jp
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Abstract

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

Keywords

uniformly locally o-minimal structurequasi-special submanifoldtype complete

MSC classification

Primary: 03C64: Model theory of ordered structures; o-minimality
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 1 , March 2023 , pp. 219 - 241
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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