Cardinality of definable families of sets in o-minimal structures

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.

I have two surnames: Andújar Guerrero. ArXiV is unable to represent this and instead considers Andújar my middle name when generating citations etc