On modal μ-calculus and non-well-founded set theory

Journal of Philosophical Logic 33 (4):343-360 (2004)
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Abstract

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal μ-calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets

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A. Tony De Luca
University of Manitoba

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Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
Non-Well-founded Sets.J. L. Bell - 1989 - Journal of Symbolic Logic 54 (3):1111-1112.
A system of axiomatic set theory - Part VII.Paul Bernays - 1954 - Journal of Symbolic Logic 19 (2):81-96.
Sts: A Structural Theory Of Sets.A. Baltag - 1999 - Logic Journal of the IGPL 7 (4):481-515.

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