Proof Search Tree and Cut Elimination
نویسنده
چکیده
A new cut elimination method is obtained here by “proof mining” (unwinding) from the following non-effective proof that begins with extracting an infinite branch B when the canonical search tree T for a given formula E of first order logic is not finite. The branch B determines a semivaluation so that B |= Ē and (*) every semivaluation can be extended to a total valuation. Since for every derivation d of E and every model M, M |= E, this provides a contradiction showing that T is finite, ∃l(T < l). A primitive recursive function L(d) such that T < L(d) is obtained using instead of (*) the statement: For every r, if the canonical search tree T r+1 with cuts of complexity r + 1 is finite, then T r is finite. In our proof the reduction of (r+1)-cuts does not introduce new r-cuts but preserves only one of the branches.
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