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Fixpoints, games and the difference hierarchy
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- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 37 / Issue 1 / January 2003
- Published online by Cambridge University Press:
- 15 November 2003, pp. 1-15
- Print publication:
- January 2003
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- Article
- Export citation
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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.
