Determinateness in the low protective hierarchy
Harvey Friedman (1971)
Fundamenta Mathematicae
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Harvey Friedman (1971)
Fundamenta Mathematicae
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Donald Matrin (1970)
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Jan Mycielski (1964)
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C. Yates (1974)
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James Henle (1981)
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Jan Mycielski (1966)
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John Burgess (1983)
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Martin, D.A. (2003)
Rendiconti del Seminario Matematico
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Ashok Maitra (1971)
Fundamenta Mathematicae
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Julian C. Bradfield (2003)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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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 . 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.