Transfinite Cardinals in Paraconsistent Set Theory

Review of Symbolic Logic 5 (2):269-293 (2012)
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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.

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10.1017/s1755020312000019

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Zach Weber
University of Otago

Citations of this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
What Counts as Evidence for a Logical Theory?Ole Thomassen Hjortland - 2019 - Australasian Journal of Logic 16 (7):250-282.

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References found in this work

In contradiction: a study of the transconsistent.Graham Priest - 2006 - New York: Oxford University Press.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.

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