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