On the definability of mad families of vector spaces

Haim Horowitz*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number103079
JournalAnnals of Pure and Applied Logic
Volume173
Issue number4
DOIs
StatePublished - Apr 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

  • Analytic sets
  • Forcing
  • Idempotent ultrafilters
  • Mad families
  • Stone-cech compactification
  • Vector spaces

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