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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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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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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EP - 232

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

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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