Some consequences of Rado’s selection lemma

Archive for Mathematical Logic 51 (7-8):739-749 (2012)

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
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DOI 10.1007/s00153-012-0296-5
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References found in this work BETA

Definability of Measures and Ultrafilters.David Pincus & Robert M. Solovay - 1977 - Journal of Symbolic Logic 42 (2):179-190.
Rado's Selection Lemma Does Not Imply the Boolean Prime Ideal Theorem.Paul E. Howard - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (9-11):129-132.
Rado's Selection Lemma Does Not Imply the Boolean Prime Ideal Theorem.Paul E. Howard - 1984 - Mathematical Logic Quarterly 30 (9‐11):129-132.
Consequences of the Axiom of Choice.Paul Howard & Jean E. Rubin - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.
The Axiom of Choice.Thomas Jech - 1973 - North-Holland.

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Citations of this work BETA

Three-Space Type Hahn-Banach Properties.Marianne Morillon - 2017 - Mathematical Logic Quarterly 63 (5):320-333.

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