A Constructive Hierarchy of Non-Well-Founded Sets
by
A.W. Roscoe
Oxford University
Coauthors: R. S. Lazic

Aczel's presentation of non-well-founded set theory works by factoring a space of directed graphs to impose extensionality. We present another construction akin to the V_\alpha hierarchy of standard set theory, in which successively richer spaces of extensional non-well-founded sets exist for each ordinal. This construction allows us to parallel many of the results and constructions of classical set theory and to compare directly the richness of the structures built at each ordinal.

One of the motivations of this theory is the understanding of the operational semantics of process algebras such as CSP and CCS in the context of infinite nondeterminism. Proofs of well-definedness over these spaces require topological arguments based on extensions of the usual restriction spaces beyond the usual countable (and hence metric) world.

Date received: April 12, 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 # caaf-70.