Bases,spanning sets,and the axiom of choice |
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| Authors: | Paul Howard |
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| Affiliation: | Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197 |
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| 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 ?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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| Keywords: | Axiom of choice vector spac basis spanning set |
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