Truth values algebras and proof normalization

Authors:
Gilles Dowek
Affiliations:
École polytechnique and INRIA, LIX, Palaiseau Cedex, France
Venue:
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Year:
2006

Citing 6
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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 B-valued model for some non trivial truth values algebra B. A theory that has a B-valued model for all truth values algebras B is said to be super-consistent. We prove that super-consistency is a model-theoretic sufficient condition for strong normalization.