Transfinite Extension of the Mu-Calculus

Julian Bradfield, Jacques Duparc, Sandra Quickert

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In [1] Bradfield found a link between finite differences formed by Σ 02 sets and the mu-arithmetic introduced by Lubarski [7]. We extend this approach into the transfinite: in allowing countable disjunctions we show that this kind of extended mu-calculus matches neatly to the transfinite difference hierarchy of Σ 02 sets. The difference hierarchy is intimately related to parity games. When passing to infinitely many priorities, it might not longer be true that there is a positional winning strategy. However, if such games are derived from the difference hierarchy, this property still holds true.
Original languageEnglish
Title of host publicationComputer Science Logic
Subtitle of host publication19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL, Oxford, UK, August 22-25, 2005. Proceedings
EditorsLuke Ong
PublisherSpringer Berlin Heidelberg
Number of pages13
ISBN (Electronic)978-3-540-31897-2
ISBN (Print)978-3-540-28231-0
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg

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