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On Modal μ-Calculus and Non-Well-Founded Set Theory

Luca Alberucci and Vincenzo Salipante
Journal of Philosophical Logic
Vol. 33, No. 4 (Aug., 2004), pp. 343-360
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226812
Page Count: 18
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On Modal μ-Calculus and Non-Well-Founded Set Theory
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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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