Truth Values Algebras and Proof Normalization

  • Gilles Dowek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4502)


We extend the notion of Heyting algebra to a notion of truth values algebra and prove that a theory is consistent if and only if it has a \(\mathcal {B}\)-valued model for some non trivial truth values algebra \(\mathcal {B}\). A theory that has a \(\mathcal {B}\)-valued model for all truth values algebras \(\mathcal {B}\) is said to be super-consistent. We prove that super-consistency is a model-theoretic sufficient condition for strong normalization.


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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gilles Dowek
    • 1
  1. 1.École polytechnique and INRIA, LIX, École polytechnique, 91128 Palaiseau CedexFrance

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