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dc.contributor.authorWEBER, Z
dc.date.available2014-05-22T04:07:48Z
dc.date.issued2010-03
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-77649233125&partnerID=40&md5=7ea716a65d737cf23c3efec6359b9455
dc.identifier.citationWEBER, Z. (2010). TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY. The Review of Symbolic Logic, 3 (1), pp.71-92. https://doi.org/10.1017/s1755020309990281.
dc.identifier.issn1755-0203
dc.identifier.urihttp://hdl.handle.net/11343/31746
dc.description.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>
dc.languageen
dc.publisherCambridge University Press (CUP)
dc.subjectPhilosophy
dc.titleTRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
dc.typeJournal Article
dc.identifier.doi10.1017/s1755020309990281
melbourne.peerreviewPeer Reviewed
melbourne.affiliationThe University of Melbourne
melbourne.affiliation.departmentPhilosophy, Anthropology and Social Inquiry
melbourne.source.titleThe Review of Symbolic Logic
melbourne.source.volume3
melbourne.source.issue1
melbourne.source.pages71-92
dc.research.codefor2203
dc.description.pagestart71
melbourne.publicationid150541
melbourne.elementsid326352
melbourne.contributor.authorWeber, Zach
melbourne.internal.ingestnoteAbstract bulk upload (2017-07-24)
dc.identifier.eissn1755-0211
melbourne.accessrightsThis item is currently not available from this repository


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