Peter Aczel.
Non-Well-Founded Sets.
CSLI. 1988
Non-well-founded structures arise in a variety of ways in the semantics
of both natural and formal languages.
Two examples are non-well-founded situations and non-terminating computational processes.
A natural modelling of such structures in set theory requires the use of non-well-founded sets.
This text presents the mathematical background to the anti-foundation axiom
and related axioms that imply the existence of non-well-founded sets when used
in place of the axiom of foundation in axiomatic set theory.