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Bases, spanning sets, and the axiom of choice

✍ Scribed by Paul Howard

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 171 KB
Volume: 53
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200610043

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Two theorems are proved: First that the statement

“there exists a field F such that for every vector space over F, every generating set contains a basis”

implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ℤ~2~ has a basis implies that every well‐ordered collection of two‐element sets has a choice function. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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