Cardinality of definable families of sets in o-minimal structures

Pablo and\'ujar Guerrero

Cardinality of definable families of sets in o-minimal structures

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arxiv 2305.12294 v1 pith:2KXKW32N submitted 2023-05-20 math.LO

Pablo Andújar Guerrero This is my paper · ORCID

classification math.LO

keywords definablecardinalityo-minimalconsequencescountingderiveexistencefamilies

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abstract

We prove that any definable family of subsets of a definable infinite set $A$ in an o-minimal structure has cardinality at most $|A|$. We derive some consequences in terms of counting definable types and existence of definable topological spaces.

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