A note on the cardinality of definable families of sets in o‐minimal structures
Abstract We prove that any definable family of subsets of a definable infinite set in an o‐minimal structure has cardinality at most . We derive some consequences in terms of counting definable types and existence of definable topological spaces.
Authors
- Pablo Andújar Guerrero (ORCID: https://orcid.org/0000-0001-5160-5366)
Institutions
- University of Leeds (GB)
Publication Details
- Journal
- Mathematical logic quarterly
- Published
- 2024-09-22
- DOI
- https://doi.org/10.1002/malq.202300030
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Engineering and Physical Sciences Research Council