A simple proof that super-consistency implies cut elimination

Abstract : We give a simple and direct proof that super-consistency implies cut elimination in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut free calculus. In particular, it gives a generalization, to all super-consistent theories, of the notion of V-complex, introduced in the semantic cut elimination proofs for simple type theory.
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https://hal.archives-ouvertes.fr/hal-00150697
Contributor : Olivier Hermant <>
Submitted on : Sunday, July 1, 2007 - 7:00:02 AM
Last modification on : Wednesday, March 27, 2019 - 4:41:26 PM
Long-term archiving on : Friday, September 21, 2012 - 4:00:18 PM

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Gilles Dowek, Olivier Hermant. A simple proof that super-consistency implies cut elimination. 2007. ⟨hal-00150697⟩

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