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TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY

Published online by Cambridge University Press:  14 January 2010

ZACH WEBER
ZACH WEBER*
Affiliation:
School of Philosophy and Historical Inquiry, University of Sydney
*
*SCHOOL OF PHILOSOPHY AND HISTORICAL INQUIRY, UNIVERSITY OF SYDNEY, NSW 2006 AUSTRALIA. E-mail:[email protected]
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Abstract

This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 1 , March 2010 , pp. 71 - 92
Copyright
Copyright © Association for Symbolic Logic 2010

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