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The Cardinal Squaring Principle and an Alternative Axiomatization of NFU

dc.contributor.authorAdlešić, Tin
dc.contributor.authorČačić, Vedran
dc.date.accessioned2024-01-04T12:38:40Z
dc.date.available2024-01-04T12:38:40Z
dc.date.issued2023-09-28
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/49162
dc.description.abstractIn this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;4en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectQuine's New Foundationsen
dc.subjectcardinal multiplicationen
dc.subjectaxiomatizationen
dc.titleThe Cardinal Squaring Principle and an Alternative Axiomatization of NFUen
dc.typeOther
dc.page.number551-581
dc.contributor.authorAffiliationAdlešić, Tin - University of Zagreb, Faculty of Teacher educationen
dc.contributor.authorAffiliationČačić, Vedran - University of Zagreb, Faculty of Scienceen
dc.identifier.eissn2449-836X
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dc.contributor.authorEmailAdlešić, Tin - tin.adlesic@ufzg.hr
dc.contributor.authorEmailČačić, Vedran - veky@math.hr
dc.identifier.doi10.18778/0138-0680.2023.25
dc.relation.volume52


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