# LFCS Seminar: Gilles Dowek

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LFCS Seminar

Pre-Heyting algebras and proof normalization.

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