A second-order system for polytime reasoning based on Grädel's theorem

@article{Cook2003ASS,
  title={A second-order system for polytime reasoning based on Gr{\"a}del's theorem},
  author={Stephen A. Cook and Antonina Kolokolova},
  journal={Ann. Pure Appl. Logic},
  year={2003},
  volume={124},
  pages={193-231}
}
We introduce a second-order system V1-Horn of bounded arithmetic formalizing polynomialtime reasoning, based on Grädel’s [11] second-order Horn characterization of P. Our system has comprehension over P predicates (defined by Grädel’s second-order Horn formulas) , and only finitely many function symbols. Other systems of polynomial-time reasoning either allow induction on NP predicates (such as Buss’s S 2 or the second-order V 1 1 ), and hence are more powerful than our system (assuming the… CONTINUE READING
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