Abstract
We consider the definability of mad families in vector spaces of the form ⨁n<ωF where F is a field of cardinality ≤ℵ0. We show that there is no analytic mad family of subspaces when F=F2, partially answering a question of Smythe. Our proof relies on a variant of Mathias forcing restricted to a certain idempotent ultrafilter whose existence follows from Glazer's proof of Hindman's theorem.
Original language | English |
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Article number | 103079 |
Journal | Annals of Pure and Applied Logic |
Volume | 173 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2022 |
Bibliographical note
Publisher Copyright:© 2021 Elsevier B.V.
Keywords
- Analytic sets
- Forcing
- Idempotent ultrafilters
- Mad families
- Stone-cech compactification
- Vector spaces