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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Unwinding a Non-effective Cut Elimination Proof
verfasst von : Grigori Mints
Erschienen in: Computer Science – Theory and Applications
Verlag: Springer Berlin Heidelberg
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Non-effective cut elimination proof uses Koenig’s lemma to obtain a non-closed branch of a proof-search tree
τ
(without cut) for a first order formula
A
, if
A
is not cut free provable. A partial model (semi-valuation) corresponding to this branch and verifying ¬
A
is extended to a total model for ¬
A
using arithmetical comprehension. This contradicts soundness, if
A
is derivable with cut. Hence
τ
is a cut free proof of
A
. The same argument works for Herbrand Theorem. We discuss algorithms of obtaining cut free proofs corresponding to this schema and quite different from complete search through all possible proofs.