A Simple Proof that Super-Consistency Implies Cut Elimination

Notre Dame Journal of Formal Logic 53 (4):439-456 (2012)
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Abstract

We give a simple and direct proof that super-consistency implies the cut-elimination property 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. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes

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Citations of this work

A Simple Proof that Super-Consistency Implies Cut Elimination.Gilles Dowek & Olivier Hermant - 2012 - Notre Dame Journal of Formal Logic 53 (4):439-456.

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References found in this work

A formulation of the simple theory of types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
Resolution in type theory.Peter B. Andrews - 1971 - Journal of Symbolic Logic 36 (3):414-432.
Hauptsatz for higher order logic.Dag Prawitz - 1968 - Journal of Symbolic Logic 33 (3):452-457.
Syntactical and semantical properties of simple type theory.Kurt Schütte - 1960 - Journal of Symbolic Logic 25 (4):305-326.

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