Hyperplanes in matroids and the axiom of choice - Université de La Réunion Accéder directement au contenu
Article Dans Une Revue Commentationes Mathematicae Universitatis Carolinae Année : 2022

Hyperplanes in matroids and the axiom of choice

Résumé

We show that in set theory without the axiom of choice ZF, the statement sH: "Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it" implies AC fin , the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC fin in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?
Fichier non déposé

Dates et versions

hal-04524324 , version 1 (28-03-2024)

Identifiants

Citer

Marianne Morillon. Hyperplanes in matroids and the axiom of choice. Commentationes Mathematicae Universitatis Carolinae, 2022, 63 (4), pp.423-441. ⟨10.14712/1213-7243.2023.010⟩. ⟨hal-04524324⟩
16 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More