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Fixpoints, games and the difference hierarchy

Published online by Cambridge University Press:  15 November 2003

Julian C. Bradfield
Julian C. Bradfield*
Affiliation:
LFCS, School of Informatics, University of Edinburgh, Edinburgh, EH9 3JZ, UK; [email protected].
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Abstract

Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over $\Sigma^0_2$. This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

Keywords

Descriptive set theoryfixpointgame quantifierinduction.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 1 , January 2003 , pp. 1 - 15
Copyright
© EDP Sciences, 2003

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