Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 53, Number 4 (2012), 439-456.
A Simple Proof that Super-Consistency Implies Cut Elimination
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.
Notre Dame J. Formal Logic, Volume 53, Number 4 (2012), 439-456.
First available in Project Euclid: 8 November 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03F05: Cut-elimination and normal-form theorems
Secondary: 03B99: None of the above, but in this section 03B15: Higher-order logic and type theory 03C90: Nonclassical models (Boolean-valued, sheaf, etc.)
Dowek, Gilles; Hermant, Olivier. A Simple Proof that Super-Consistency Implies Cut Elimination. Notre Dame J. Formal Logic 53 (2012), no. 4, 439--456. doi:10.1215/00294527-1722692. https://projecteuclid.org/euclid.ndjfl/1352383225