A Concrete Final Coalgebra Theorem for ZF Set Theory

@inproceedings{Paulson1994ACF,
title={A Concrete Final Coalgebra Theorem for ZF Set Theory},
author={Lawrence C. Paulson},
booktitle={TYPES},
year={1994}
}

A special final coalgebra theorem, in the style of Aczel’s [2], is proved within standard Zermelo-Fraenkel set theory. Aczel’s AntiFoundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s Solution and Substitution Lemmas are proved in the style of Rutten and Turi [12]. The approach is less general than Aczel’s, but the… CONTINUE READING