Some consequences of Rado’s selection lemma

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

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
Categories (categorize this paper)
DOI 10.1007/s00153-012-0296-5
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,373
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

Add more references

Citations of this work BETA

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

Add more citations

Similar books and articles

Canonical Partition Relations.James E. Baumgartner - 1975 - Journal of Symbolic Logic 40 (4):541-554.
Π01-Classes and Rado's Selection Principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684 - 693.
Operant Behavior and the Thesis of “Selection by Consequences”.J. Moore - 2001 - Behavioral and Brain Sciences 24 (3):546-547.
Erdös-Rado Without Choice.Thomas Forster - 2007 - Journal of Symbolic Logic 72 (3):897 - 900.
Some New Intuitionistic Equivalents of Zorn’s Lemma.John L. Bell - 2003 - Archive for Mathematical Logic 42 (8):811-814.
The Non-Existence of a Principle of Natural Selection.Abner Shimony - 1989 - Biology and Philosophy 4 (3):255-273.
Selection: Information and Replication of the Operant.Ralph Spiga - 2001 - Behavioral and Brain Sciences 24 (3):556-557.
A More Pluralist Typology of Selection Processes.Bence Nanay - 2001 - Behavioral and Brain Sciences 24 (3):547-548.
Multi-Level Selection, Covariance and Contextual Analysis.Samir Okasha - 2004 - British Journal for the Philosophy of Science 55 (3):481-504.


Added to PP index

Total views
4 ( #1,142,341 of 2,286,177 )

Recent downloads (6 months)
1 ( #842,961 of 2,286,177 )

How can I increase my downloads?


My notes

Sign in to use this feature