Predicativity, Circularity, and Anti-Foundation
Michael Rathjen · 2004
Abstract. The anti-foundation axiom, AFA, has turned out to be a versatile principle in set theory for modelling a plethora of circular and self-referential phenomena. This paper explores whether AFA and the most important tools emanating from it, such as the solution lemma and the co-recursion principle, can be developed on predicative grounds, that is to say, within a predicative theory of sets. If one could show that most of the circular phenomena that have arisen in computer science do not require impredicative set existence axioms for their modelling, this would demonstrate that their circularity is of a different kind than the one which underlies impredicative definitions. 1.