TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
Source TitleReview of Symbolic Logic
PublisherCambridge University Press (CUP)
University of Melbourne Author/sWeber, Zach
AffiliationPhilosophy, Anthropology and Social Inquiry
Document TypeJournal Article
CitationsWEBER, Z. (2010). TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY. The Review of Symbolic Logic, 3 (1), pp.71-92. https://doi.org/10.1017/s1755020309990281.
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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.
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