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.

Peter Aczel is reader in mathematical logic at Manchester University

- Foreword
- Preface
- Introduction
## Part One The Anti-Foundation Axiom

- 1 Introducing the Axiom
- 2 The Axiom in More Detail
- 3 A Model of the Axiom
## Part Two Variants of the Anti-Formation Axiom

- 4 Variants Using a Regular Bisimulation
- 5 Another Variant
## Part Three On Using the Anti-Foundation Axiom

- 6 Fixed Points of Set Continuous Operators
- 7 The Special Final Coalgebra Theorem
- 8 An Application to Communicating Systems
## Appendices

- A Notes Towards a History
- B Background Set Theory
- References
- Index of Definitions
- Index of Axioms and Results

5/1/88

ISBN (Paperback): 9780937073223 (0937073229)

ISBN (Electronic): 9781575867564 (1575867567)

Subject: Linguistics; Logic; Context

Subject: Mathematics; Axiomatic Set Theory