1521-3870/asset/2256_left.gif?v=1&s=becebab9c3e85769a14b145f17b8e337848bc48b)
1521-3870/asset/2256_right.gif?v=1&s=6d251fa351b8e0943ed3dc42b2beb251d4cbfa3e)
Original Paper
The axiom of choice and the law of excluded middle in weak set theories
Article first published online: 7 MAR 2008
DOI: 10.1002/malq.200710030
Copyright © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
Bell, J. L. (2008), The axiom of choice and the law of excluded middle in weak set theories. Mathematical Logic Quarterly, 54: 194–201. doi: 10.1002/malq.200710030
Publication History
- Issue published online: 7 MAR 2008
- Article first published online: 7 MAR 2008
- Manuscript Accepted: 22 AUG 2007
- Manuscript Revised: 19 AUG 2007
- Manuscript Received: 28 MAR 2007
- Abstract
- References
- Cited By
Keywords:
- Axiom of choice;
- axiom of extensionality;
- weak set theory;
- law of excluded middle
Abstract
A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)