拟阵中的超平面与选择公理

IF 0.2 Q4 MATHEMATICS Commentationes Mathematicae Universitatis Carolinae Pub Date : 2023-04-28 DOI:10.14712/1213-7243.2023.010

Marianne Morillon

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引用次数: 0

摘要

.我们证明了在没有选择公理ZF的集合论中，陈述sH:（cid:16）一个（cid:28）nitary拟阵的每个适当闭子集是包括它（cid:17）的超平面的交集暗示了AC fin，（非空）（cid:28）nite集的选择公理。我们还根据（cid:16）图（cid:17）拟阵提供了一个等价于语句AC fin的语句。ZF中有几个悬而未决的问题，例如：sH是否意味着选择公理？

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hyperplanes in matroids and the axiom of choice

. We show that in set-theory without the axiom of choice ZF , the statement sH : (cid:16)Every proper closed subset of a (cid:28)nitary matroid is the intersection of hyperplanes including it(cid:17) implies AC ﬁn , the axiom of choice for (nonempty) (cid:28)nite sets. We also provide an equivalent of the statement AC ﬁn in terms of (cid:16)graphic(cid:17) matroids. Several open questions stay open in ZF , for example: does sH imply the Axiom of Choice?

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