Binary Relations as a Foundation of Mathematics


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. ISBN 9789090224466

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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.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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