Consistency Without Cut Elimination

Publication date: 24 October 2002

Abstract: In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It also shows how finitaryness (in the sense of finite choice of premises for each rule) is actually a triviality (contrarily to what one would guess from textbooks).

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Proof theory in general (including proof-theoretic semantics) (03F03)

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