Church's set theory
by
Thomas Forster
Cambridge University

Many years ago the independence of the axiom of foundation from the other axioms of set theory was proved by by a technique which involved replacing the membership relation in by in composed with a judiciously chosen permutation of the universe. In one of his lesser-known contributions to logic Church elaborated this into a richer technique that gave a consistency proof for a set theory with a universal set. In this paper based on the author's article for the Church 90th birthday festschrift a sketch of the method is given and a summary of what is known about what it can do. The talk will concentrate on ideas and the proofs will be largely relegated to an acompanying handout.

Date received: March 7, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caac-04.