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.
|Title of host publication||Reflections on Type Theory, Lambda Calculus, and the Mind: Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday|
|Editors||E. Barendsen, V. Capretta, H. Geuvers, M. Niqui|
|Place of Publication||Nijmegen|
|Number of pages||14|
|Publication status||Published - 17 Dec 2007|