If vector spaces are projective modules then multiple choice holds

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 2005 English Publisher:WileyJournal:MLQ, volume 51, pages 187-190 (issn: 0942-5616, eissn: 1521-3870,

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Authors: Paul E. Howard;

doi: 10.1002/malq.200410018

If vector spaces are projective modules then multiple choice holds

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Abstract

Summary: We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.

Related Organizations

Eastern Michigan University
United States

Keywords

projective module, Axiom of choice and related propositions, vector space, Axiom of multiple choice

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