TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
Author
WEBER, ZDate
2010-03Source Title
The Review of Symbolic LogicPublisher
Cambridge University Press (CUP)University of Melbourne Author/s
Weber, ZachAffiliation
Philosophy, Anthropology and Social InquiryMetadata
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Journal ArticleCitations
WEBER, Z. (2010). TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY. The Review of Symbolic Logic, 3 (1), pp.71-92. https://doi.org/10.1017/s1755020309990281.Access Status
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<jats:p>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.</jats:p>
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