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# The Undecidability of k-Provability

@article{Buss1991TheUO, title={The Undecidability of k-Provability}, author={Samuel R. Buss}, journal={Ann. Pure Appl. Logic}, year={1991}, volume={53}, pages={75-102} }

- Published 1991 in Ann. Pure Appl. Logic
DOI:10.1016/0168-0072(91)90059-U

Buss, S.R., The undecidability of k-provability, Annals of Pure and Applied Logic 53 (1991) 75-102. The k-provability problem is, given a first-order formula 4 and an integer k, to determine if @ has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the k-provability problem for the sequent calculus is undecidable. Indeed, for every r.e. set X there is a formula @(I) and an integer k such that for all n, $(SnO) has a proof of Sk sequents if and only if n… CONTINUE READING