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TRANSFINITE CARDINALS IN PARACONSISTENT SET THEORY

Published online by Cambridge University Press:  29 March 2012

ZACH WEBER
ZACH WEBER*
Affiliation:
University of Otago; University of Melbourne
*
*DEPARTMENT OF PHILOSOPHY, PO BOX 56, UNIVERSITY OF OTAGO, DUNEDIN 9054, NEW ZEALAND. E-mail:zach.weber@otago.ac.nz
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Abstract

This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 269 - 293
Copyright
Copyright © Association for Symbolic Logic 2012

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