Cardinality of definable families of sets in o-minimal structures

Pablo Andújar Guerrero

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arXiv · 2305.12294

Cardinality of definable families of sets in o-minimal structures

Pablo Andújar Guerrero

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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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BibTeX RIS

Pablo Andújar Guerrero. 2023-05-20. Cardinality of definable families of sets in o-minimal structures. https://arxiv.org/abs/2305.12294

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