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Fixpoint Alternation and the Game Quantifier

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Computer Science Logic (CSL 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1683))

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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 ∑ 02 . 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.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Bygning 540, Ny Munkegade, 8000, Århus C, Denmark

    J. C. Bradfield

  2. LFCS†, Division of Informatics, University of Edinburgh, Edinburgh, UK, EH9 3JZ

    J. C. Bradfield

Authors
  1. J. C. Bradfield
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104, Freiburg, Germany

    Jörg Flum

  2. Dpto. de Sistemas Informáticos y Programación Edificio Fac. Matemáticas, Universidad Complutense de Madrid, Av. Complutense s/n, E-28040, Madrid, Spain

    Mario Rodriguez-Artalejo

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© 1999 Springer-Verlag Berlin Heidelberg

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Bradfield, J.C. (1999). Fixpoint Alternation and the Game Quantifier. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_25

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  • DOI: https://doi.org/10.1007/3-540-48168-0_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66536-6

  • Online ISBN: 978-3-540-48168-3

  • eBook Packages: Springer Book Archive

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