Abstract
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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Dowek, G. (2007). Truth Values Algebras and Proof Normalization. In: Altenkirch, T., McBride, C. (eds) Types for Proofs and Programs. TYPES 2006. Lecture Notes in Computer Science, vol 4502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74464-1_8
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DOI: https://doi.org/10.1007/978-3-540-74464-1_8
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