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References

  1. S. Buss,Bounded Arithmetic (Bibliopolis, Napoli, 1986).

    Google Scholar 

  2. S. Buss, Axiomatization and conservation results for fragments of bounded arithmetic, to appear in:Contemporary Mathematics AMS vol. 106, Proc. Workshop in Logic and Computation (1990) pp. 57–84

  3. H. Gaifman and C. Dimitracopoulos, Fragments of Peano's arithmetic and the MRDP theorem,Logic et Algorithmic, Monogr. No. 30 de l'Enseignement Mathématique, Genève (1982) pp. 187–206.

  4. J. Krajíček, π1-conservativeness in systems of bounded arithmetic, typescript (1988).

  5. J. Krajíček, Exponentiation and second order bounded arithmetic, Ann. Pure Appl. Logic 48 (1990) 261–276.

    Google Scholar 

  6. J. Krajíček and P. Pudlák, Quantified propositional calculi and fragments of bounded arithmetic, Zeit. Math. Logik and Grandlog. 36(1) (1990) 29–46.

    Google Scholar 

  7. J. Krajíček, P. Pudlák and G. Takeuti, Bounded arithmetic and the polynomial hierarchy, Ann. Pure Appl. Logic 52 (1991) 143–153.

    Google Scholar 

  8. J. Paris and C. Dimitracopoulos, Truth definition forΔ 0 formulae,Logic et Algorithmic, Monogr. No. 30 de l'Enseignement Mathématique, Genéve (1982) pp. 317–330.

  9. J. Paris and A. Wilkie, On the scheme of induction for bounded arithmetic formulas, Ann. Pure Appl. Logic 35(3) (1987) 261–302.

    Google Scholar 

  10. G. Takeuti, Bounded arithmetic and truth definition, Ann. Pure Appl. Logic 39(1) (1988) 75–104.

    Google Scholar 

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Krajíček, J., Takeuti, G. On induction-free provability. Ann Math Artif Intell 6, 107–125 (1992). https://doi.org/10.1007/BF01531024

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