Non-Well-Founded Sets (Center for the Study of Language and Information - Lecture Notes): Peter Aczel

Description

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 modeling 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.
Table of Contents
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-Foundation 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 Named Axioms and Results

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