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Non-Well-Founded Sets

Peter Aczel

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


ISBN (Paperback): 9780937073223 (0937073229)
ISBN (Electronic): 9781575867564 (1575867567)
Subject: Linguistics; Logic; Context

Subject: Mathematics; Axiomatic Set Theory

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