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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?
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Preprints, Working Papers, ...
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https://hal.univ-reunion.fr/hal-03426458
Contributor : Marianne Morillon Connect in order to contact the contributor
Submitted on : Friday, November 12, 2021 - 11:56:13 AM
Last modification on : Wednesday, November 24, 2021 - 3:31:50 AM

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SH2ACfin_oct21.pdf
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  • HAL Id : hal-03426458, version 1

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

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