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The axiom of choice for well-ordered families and for families of well-orderable sets

Published online by Cambridge University Press:  12 March 2014

Paul Howard  and
Jean E. Rubin
Paul Howard
Affiliation:
Eastern Michigan University, Department of Mathematics, Ypsilanti, Michigan 48197, E-mail: phoward@emunix.emich.edu Purdue University, Department of Mathematics, West Lafayette, Indiana 47907-1395, E-mail: jer@math.purdue.edu
Jean E. Rubin
Affiliation:
Purdue University, Department of Mathematics, West Lafayette, Indiana 47907-1395, E-mail: jer@math.purdue.edu
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Abstract

We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets of well-orderable sets are both true, but the axiom of choice is false.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 4 , December 1995 , pp. 1115 - 1117
Copyright
Copyright © Association for Symbolic Logic 1995

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References

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