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Journal of Philosophical Logic

, Volume 35, Issue 3, pp 225–230 | Cite as

Note on Some Fixed Point Constructions in Provability Logic

  • Per Lindström
Article

Abstract

We present a quite simple proof of the fixed point theorem for GL. We also use this proof to show that Sambin's algorithm yields a fixed point.

Key Words

fixed point GL Sambin's algorithm 

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References

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    Boolos, G.: The Unprovability of Consistency, Cambridge University Press, 1979.Google Scholar
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    Boolos, G.: The Logic of Provability, Cambridge University Press, 1993.Google Scholar
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    Lindström, P.: Provability logic – a short introduction, Theoria 62 (1996), 19–61.CrossRefGoogle Scholar
  4. 4.
    Sambin, G.: An effective fixed point theorem in intuitionistic diagonalizable algebras, Stud. Log., 35 (1976), 345–361.CrossRefGoogle Scholar
  5. 5.
    Sambin, G. and Valentini, S.: The modal logic of provability. The sequential approach, J. Philos. Logic, 11 (1982), 311–342.CrossRefGoogle Scholar
  6. 6.
    Smorynski, C.: Self-Reference and Modal Logic, Springer, 1985.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Gatan 3TolleredSweden

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