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December 2002 Zermelo's Cantorian Theory of Systems of Infinitely Long Propositions
R. Gregory Taylor
Bull. Symbolic Logic 8(4): 478-515 (December 2002). DOI: 10.2178/bsl/1182353918

Abstract

In papers published between 1930 and 1935. Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed "Cantorian" in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate highly transfinite concepts of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous.

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R. Gregory Taylor. "Zermelo's Cantorian Theory of Systems of Infinitely Long Propositions." Bull. Symbolic Logic 8 (4) 478 - 515, December 2002. https://doi.org/10.2178/bsl/1182353918

Information

Published: December 2002
First available in Project Euclid: 20 June 2007

zbMATH: 1040.03003
MathSciNet: MR1956866
Digital Object Identifier: 10.2178/bsl/1182353918

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.8 • No. 4 • December 2002
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