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Mathematics > Logic
Title: Types, transversals and definable compactness in o-minimal structures
(Submitted on 6 Nov 2021)
Abstract: Through careful analysis of types inspired by [AGTW21] we characterize a notion of definable compactness for definable topologies in general o-minimal structures, generalizing results from [PP07] about closed and bounded definable sets in o-minimal expansions of ordered groups. Along the way we prove a parameter version for o-minimal theories of the connection between dividing and definable types known in the more general dp-minimal context [SS14], through an elementary proof that avoids the use of existing forking and VC literature. In particular we show that, if an $A$-definable family of sets has the $(p,q)$-property, for some $p\geq q$ with $q$ large enough, then the family admits a partition into finitely many subfamilies, each of which extends to an $A$-definable type.
Submission history
From: Pablo Andújar Guerrero [view email][v1] Sat, 6 Nov 2021 04:38:59 GMT (67kb,D)
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