# On Gödel's Theorems on Lenghts of Proofs I: Number of Lines and Speedup for Arithmetics

@article{Buss1994OnGT, title={On G{\"o}del's Theorems on Lenghts of Proofs I: Number of Lines and Speedup for Arithmetics}, author={S. Buss}, journal={J. Symb. Log.}, year={1994}, volume={59}, pages={737-756} }

This paper discusses lower bounds for proof length, especially as measured by number of steps (inferences). We give the first publicly known proof of Godel's claim that there is superrecursive (in fact, unbounded) proof speedup of ( i + l)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… Expand

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