Gödel Logics and Cantor-Bendixon Analysis

  • Norbert Preining
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2514)


This paper presents an analysis of Gödel logics with countable truth value sets with respect to the topological and order theoretic structure of the underlying truth value set. Gödel logics have taken an important rôle in various areas of computer science, e.g. logic programming and foundations of parallel computing. As shown in a forthcoming paper all these logics are not recursively axiomatizable. We show that certain topological properties of the truth value set can distinguish between various logics. Complete separation of a class of countable valued logics will be proven and direction for further separation results given.


Limit Point Polish Space Truth Function Topological Type Separation Result 
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  1. [Baa96]
    M. Baaz. Infinite-valued Gödel logics with 0-1-projections and relativizations. In Gödel 96. Kurt Gödel’s Legacy, volume 6 of LNL, pages 23–33, 1996.Google Scholar
  2. [BV98]
    M. Baaz and H. Veith. An axiomatization of quantified propositional Gödel logic using the Takeuti-Titani rule. volume 13 of LNML, pages 91–104, 1998.Google Scholar
  3. [Dum59]
    M. Dummett. A propositional logic with denumerable matrix. J. of Symbolic Logic, 24:96–107, 1959.MathSciNetGoogle Scholar
  4. [Göd33]
    K. Gödel. Zum Intuitionistischen Aussagenkalkül. Ergebnisse eines mathematischen Kolloquiums, 4:34–38, 1933.Google Scholar
  5. [Háj98]
    P. Hájek. Metamathematics of Fuzzy Logic. Kluwer, 1998.Google Scholar
  6. [Kec95]
    Alexander S. Kechris. Classical Descriptive Set Theory. Springer, 1995.Google Scholar
  7. [Win99]
    Reinhard Winkler. How much must an order theorist forget to become a topologist? In Contributions of General Algebra 12, Proc. of the Vienna Conference, Klagenfurt, Austria, 1999. Verlag Johannes Heyn.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Norbert Preining
    • 1
  1. 1.Institute for Algebra and Computational MathematicsUniversity of TechnologyViennaAustria

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