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Preprints, Working Papers, ... Year : 2021

Hyperplanes in matroids ans the Axiom of Choice

Abstract

We show that in set-theory without the axiom of choice ZF, the statement sH: Every proper closed subset of a nitary matroid is the intersection of hyperplanes including it implies AC fin , the axiom of choice for (nonempty) nite 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?

Domains

Logic [math.LO]
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Dates and versions

hal-03426458 , version 1 (12-11-2021)

Identifiers

  • HAL Id : hal-03426458 , version 1

Cite

Marianne Morillon. Hyperplanes in matroids ans the Axiom of Choice. 2021. ⟨hal-03426458⟩
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