On induction-free provability

@article{Krajcek1992OnIP,
  title={On induction-free provability},
  author={Jan Kraj{\'i}cek and Gaisi Takeuti},
  journal={Annals of Mathematics and Artificial Intelligence},
  year={1992},
  volume={6},
  pages={107-125}
}
In this article we study relations between various fragments of bounded arithmetic. The fragments of interest bere are the theories S~ and T~ introduced by Buss in [1]. The reader may recall that the principal axioms of S~ resp. of T~ are !t-PIND resp. !t-IND axioms, where the former are instances of polynomially bounded inducton for !t-formulas while the latter are instances of ordinary induction for !t-formulas. Indications of the significance of these theories for complexity theory are two… CONTINUE READING
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