Binary Relations as a Foundation of Mathematics

Jan Kuper

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    We describe a theory for binary relations in the Zermelo-Fraenkel style. We choose for ZFCU, a variant of ZFC Set theory in which the Axiom of Foundation is replaced by an axiom allowing for non-wellfounded sets. The theory of binary relations is shown to be equi-consistent ZFCU by constructing a model for the theory of binary relations in ZFU and vice versa. Thus, binary relations are a foundation for mathematics in the same sense as sets are.
    Original languageUndefined
    Title of host publicationReflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday
    EditorsE. Barendsen, V. Capretta, H. Geuvers, M. Niqui
    Place of PublicationNijmegen
    PublisherRadboud University
    Number of pages14
    ISBN (Print)978-90-9022446-6
    Publication statusPublished - 17 Dec 2007

    Publication series

    PublisherRadboud University


    • IR-64509
    • EWI-11511
    • METIS-245832

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