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Extending Independent Sets to Bases and the Axiom of Choice

✍ Scribed by Kyriakos Keremedis

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 363 KB
Volume: 44
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19980440106

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✦ Synopsis

Abstract

We show that the both assertions “in every vector space B over a finite element field every subspace V ⊆ B has a complementary subspace S” and “for every family 𝒜 of disjoint odd sized sets there exists a subfamily ℱ={F~j~:j ϵω} with a choice function” together imply the axiom of choice AC. We also show that AC is equivalent to the statement “in every vector space over ℚ every generating set includes a basis”.

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