Binary Relations as a Foundation of Mathematics

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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    Abstract

    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
    Pages223-232
    Number of pages14
    ISBN (Print)978-90-9022446-6
    Publication statusPublished - 17 Dec 2007

    Publication series

    Name
    PublisherRadboud University
    NumberSupplement

    Keywords

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

    Cite this

    Kuper, J. (2007). Binary Relations as a Foundation of Mathematics. In E. Barendsen, V. Capretta, H. Geuvers, & M. Niqui (Eds.), Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday (pp. 223-232). Nijmegen: Radboud University.
    Kuper, Jan. / Binary Relations as a Foundation of Mathematics. Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday. editor / E. Barendsen ; V. Capretta ; H. Geuvers ; M. Niqui. Nijmegen : Radboud University, 2007. pp. 223-232
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    title = "Binary Relations as a Foundation of Mathematics",
    abstract = "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.",
    keywords = "IR-64509, EWI-11511, METIS-245832",
    author = "Jan Kuper",
    year = "2007",
    month = "12",
    day = "17",
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    isbn = "978-90-9022446-6",
    publisher = "Radboud University",
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    Kuper, J 2007, Binary Relations as a Foundation of Mathematics. in E Barendsen, V Capretta, H Geuvers & M Niqui (eds), Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday. Radboud University, Nijmegen, pp. 223-232.

    Binary Relations as a Foundation of Mathematics. / Kuper, Jan.

    Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday. ed. / E. Barendsen; V. Capretta; H. Geuvers; M. Niqui. Nijmegen : Radboud University, 2007. p. 223-232.

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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    T1 - Binary Relations as a Foundation of Mathematics

    AU - Kuper, Jan

    PY - 2007/12/17

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    N2 - 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.

    AB - 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.

    KW - IR-64509

    KW - EWI-11511

    KW - METIS-245832

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    SP - 223

    EP - 232

    BT - Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday

    A2 - Barendsen, E.

    A2 - Capretta, V.

    A2 - Geuvers, H.

    A2 - Niqui, M.

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    Kuper J. Binary Relations as a Foundation of Mathematics. In Barendsen E, Capretta V, Geuvers H, Niqui M, editors, Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday. Nijmegen: Radboud University. 2007. p. 223-232