Polynomially and superexponentially shorter proofs in fragments of arithmetic

Journal of Symbolic Logic 57 (3):844-863 (1992)
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Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
The modal logic of provability. The sequential approach.Giovanni Sambin & Silvio Valentini - 1982 - Journal of Philosophical Logic 11 (3):311 - 342.
On me number of steps in proofs.Jan Krajíèek - 1989 - Annals of Pure and Applied Logic 41 (2):153-178.
On the number of steps in proofs.Jan Kraj\mIček - 1989 - Annals of Pure and Applied Logic 41 (2):153-178.
Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.

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