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    TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY

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    Author
    WEBER, Z
    Date
    2010-03
    Source Title
    The Review of Symbolic Logic
    Publisher
    Cambridge University Press (CUP)
    University of Melbourne Author/s
    Weber, Zach
    Affiliation
    Philosophy, Anthropology and Social Inquiry
    Metadata
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    Document Type
    Journal Article
    Citations
    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
    This item is currently not available from this repository
    URI
    http://hdl.handle.net/11343/31746
    DOI
    10.1017/s1755020309990281
    Abstract
    <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>
    Keywords
    Philosophy

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