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TRANSFINITE CARDINALS IN PARACONSISTENT SET THEORY

  • ZACH WEBER (a1)
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.

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*DEPARTMENT OF PHILOSOPHY, PO BOX 56, UNIVERSITY OF OTAGO, DUNEDIN 9054, NEW ZEALAND. E-mail:zach.weber@otago.ac.nz
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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