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}
}
  • S. Buss
  • Published 1994
  • Mathematics, Computer Science
  • J. Symb. Log.
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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This paper discusses a claim made by Godel in a letter to von Neumann which is closely related to the P versus NP problem. Godel’s claim is that k-symbol provability in first-order logic can not beExpand
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Publisher Summary This chapter focuses on the length of proofs of finitistic consistency statements in first order theories. By the second incompleteness theorem of Godel, a sufficiently rich theoryExpand
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ABSTRACT. Given a theory T, let \-^A mean "A has a proof in T of at most k lines". We consider a formulation PA* of Peano arithmetic withfull induction but addition and multiplication being ternaryExpand
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The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts ofExpand
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The purpose of this note is to state precisely and prove the following informal statement: If T is a theory and a is a new axiom such that r + n o n a is an undecidable theory then some theorems of TExpand
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