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ω-categorical weakly o-minimal expansions of Boolean lattices

✍ Scribed by Stefano Leonesi; Carlo Toffalori

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 150 KB
Volume: 49
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310042

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✦ Synopsis

Abstract

We study ω‐categorical weakly o‐minimal expansions of Boolean lattices. We show that a structure 𝒜 = (A,≤, ℐ) expanding a Boolean lattice (A,≤) by a finite sequence I of ideals of A closed under the usual Heyting algebra operations is weakly o‐minimal if and only if it is ω‐categorical, and hence if and only if A/I has only finitely many atoms for every I ∈ ℐ. We propose other related examples of weakly o‐minimal ω‐categorical models in this framework, and we examine the internal structure of these models.

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## Abstract We consider the sets definable in the countable models of a weakly o‐minimal theory __T__ of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic (hence __T__ is p‐__ω__‐categorical), in other words when each of these definable sets adm