Archive for Mathematical Logic

, Volume 51, Issue 7–8, pp 739–749 | Cite as

Some consequences of Rado’s selection lemma

Article

Abstract

We prove in set theory without the Axiom of Choice, that Rado’s selection lemma (\({\mathbf{RL}}\)) implies the Hahn-Banach axiom. We also prove that \({\mathbf{RL}}\) is equivalent to several consequences of the Tychonov theorem for compact Hausdorff spaces: in particular, \({\mathbf{RL}}\) implies that every filter on a well orderable set is included in a ultrafilter. In set theory with atoms, the “Multiple Choice” axiom implies \({\mathbf{RL}}\) .

Keywords

Axiom of choice Product topology Compactness Rado’s selection lemma Hahn-Banach 

Mathematics Subject Classification (2000)

Primary 03E25 Secondary 54B10 46A22 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.ERMIT, Département de Mathématiques et InformatiqueUniversité de La RéunionSainte-ClotildeFrance

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