• Corpus ID: 10794773

Comments on Beckmann's Uniform Reducts

@article{Cook2006CommentsOB,
  title={Comments on Beckmann's Uniform Reducts},
  author={Stephen A. Cook},
  journal={ArXiv},
  year={2006},
  volume={abs/cs/0601086}
}
  • S. Cook
  • Published 19 January 2006
  • Computer Science, Mathematics
  • ArXiv
Arnold Beckmann defined the uniform reduct of a propositional proof system f to be the set of those bounded arithmetical formulas whose propositional translations have polynomial size f-proofs. We prove that the uniform reduct of f + Extended Frege consists of all true bounded arithmetical formulas iff f + Extended Frege simulates every proof system. 

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We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the
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TLDR
The problem of the length of proofs of statements in finitely, axiomatized theory S is studied, in relation with problems of propositional proof systems.
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