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    If the empty sequent is not deducible, then Z_2 is consis... — Carmelics
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    Supports→The consistency of second-order arithmetic (Z_2) is entailed by Takeuti's Fundamental Conjecture

    If the empty sequent is not deducible, then Z_2 is consistent

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    Cut elimination holding for GLC (or its fragment GLC2 corresponding to Z_2) rule...Takeuti's Fundamental Conjecture asserts that cut elimination holds for GLCThe consistency of second-order arithmetic (Z_2) is entailed by Takeuti's Fundam...

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    The empty sequent is not provable82%Cut elimination holding for GLC (or its fragment GLC2 corresponding to...82%If the empty sequent were provable, it would have a cut-free derivatio...79%A cut-free derivation of the empty sequent can contain only empty sequ...77%

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    As the deducibility of the empty sequent is ruled out if cut elimination holds for GLC (or just the fragment GLC2 corresponding to \(\bZ_2\)), Takeuti’s Fundamental Conjecture entails the consistency of \(\bZ_2\). However note that it does not yield the subformula property as in the first-order case since the minor formula \(F(\{x\mid A(x)\})\) in \((\exists_2\,\rR)\) and \((\forall_2\,\bL)\) may have a much higher (quantifier) complexity than the principal formula \(\exists XF(X)\) and \(\foral

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