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Abstract: This paper discusses lower bounds for proof length, especially as measured by number of steps (inferences). We give the first publicly known proof of Gödel's claim that there is superrecursive (in fact, unbounded) proof speedup of (i + 1)-st order arithmetic over i-th order arithmetic, where arithmetic is formalized in Hilbert-style calculi with + and as function symbols or with the language of PRA. The same results are established for any weakly schematic formalization of higher-order logic;... (Update)
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BibTeX entry: (Update)
@misc{ buss-gdels,
author = "Samuel R. Buss",
title = "On G{\"o}del's Theorems on Lengths of Proofs {I}: Number of Lines and Speedup
for Arithmetics",
url = "citeseer.ist.psu.edu/511808.html" }
Citations (may not include all citations):370 A Mathematical Introduction to Logic (context) - Enderton - 1972
72 North-Holland (context) - Takeuti, Theory - 1987
28 Annals of Pure and Applied Logic (context) - cek, number et al. - 1989
20 Transactions of the American Mathematical Society (context) - Parikh, on et al. - 1973
17 the scheme of induction for bounded arithmetic formulas (context) - Wilkie, Paris - 1987
9 the lengths of proofs of finitistic consistency statements i.. (context) - ak - 1986
8 Abbreviating proofs by adding new axioms (context) - Ehrenfeucht, Mycielski - 1971
7 The number of proof lines and the size of proofs in first-or.. (context) - cek, ak - 1988
6 A unification-theoretic method for investigating the k-prova.. (context) - Farmer - 1991
4 On Godel's theorems on lengths of proofs II: Lower bounds fo.. (context) - Buss
3 Uber die Lange von Beweisen (context) - odel - 1936
2 Sentences Undecidable in Formalized Arithmetic: An Expositio.. (context) - Mostowski - 1952
1 Introductory note to (context) - to - 1936
1 Speed-up by theories with infinite models (context) - Statman - 1981
1 Some applications of formalized consistency proofs (context) - Kreisel, Wang - 1955
Documents on the same site (ftp://euclid.ucsd.edu/pub/sbuss/research/): More
Ordinal Notations and Well-Orderings in Bounded Arithmetic - Beckmann, Buss, Pollett (2000) (Correct)
On the Computational Content of Intuitionistic Propositional .. - Buss, Pudlák (2000) (Correct)
Minimum Propositional Proof Length is NP-Hard to.. - Alekhnovich, Buss.. (1998) (Correct)
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