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Length and Structure of Proofs

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REFERENCES

  • Buss, S.: 1991, ‘The Undecidability of k-Provability’, Annals of Pure and Applied Logic 53, 75–102.

    Google Scholar 

  • Buss, S.: 1994, ‘On Gödel's Theorems on Lengths of Proofs I: Number of Lines and Speedup for Arithmetics’, J. Symb. Logic 59, 737–756.

    Google Scholar 

  • Buss, S.: 1998a, ‘An Introduction to Proof Theory’, in S. Buss (ed.), Handbook of Proof Theory, North Holland, pp. 1–78. (To appear).

  • Buss, S.: 1998b ‘First-Order Proof Theory of Arithmetic’, in S. Buss (ed.), Handbook of Proof Theory, North-Holland, pp. 79–147. (To appear).

  • Pudlák, P. and S. R. Buss: 1995, ‘How to Lie Without Being (Easily) Convicted and the Lengths of Proofs in Propositional Calculus’, in Pacholski and Tiuryn (eds.), 8th Workshop on Computer Science Logic, Kazimierz, Poland, September 1994, Springer-Verlag Lecture Notes in Computer Science # 933, pp. 151–62.

  • Carbone, A.: 1993, On Logical Flow Graphs, Doctoral Thesis, City University of New York.

  • Carbone, A.: 1996, ‘The Craig Interpolation Theorem for Schematic Systems’, Collegium Logicum, Vol. 2, Annals of the Kurt Gödel Society, Springer-Verlag.

  • Carbone, A.: forthcoming, ‘Interpolants, Cut Elimination and Flow Graphs’, in the Annals of Pure and Applied Logic.

  • Cook, S.: 1971, ‘The Complexity of Theorem Proving Procedures’, Proceedings of 3rd ACM Symposium on the Theory of Computing, pp. 151–58.

  • Cook, S. and A. Rekhow: 1979, ‘The Relative Efficiency of Proof Systems’, J. Symb. Logic 44, 36–60.

    Google Scholar 

  • Ehrenfeucht, A. and J. Mycielski: 1971, ‘Abbreviating Proofs by Adding New Axioms’, Bull. Amer. Math. Soc. 77, 366–367.

    Google Scholar 

  • Girard, J. Y.: 1987, ‘Linear Logic’, Theoretical Computer Science 50, 1–102.

    Google Scholar 

  • Gödel, K.: 1986, ‘On the Length of Proofs’, in Feferman et al. (eds.), The Collected Works of K. Gödel, Vol. 1, Oxford, pp. 394–99.

  • Goldfarb, W.: 1981, ‘The Undecidability of the Second Order Unification Problem’, Theoretical Computer Science 13, 225–30.

    Google Scholar 

  • Krajicek, J.: 1995, ‘On Frege and Extended Frege Proof Systems’, in P. Clote and J. Remmel (eds.), Feasible Mathematics II, Birkäuser, pp. 284–319.

  • Krajicek, J.: 1995, Bounded Arithmetic, Propositional Logic and Complexity Theory, Cambridge University Press, Cambridge.

    Google Scholar 

  • Parikh, R.: 1971, ‘Existence and Feasibility in Arithmetic’, J. Symbolic Logic 36, 494–508.

    Google Scholar 

  • Parikh, R.: 1973, ‘On the Length of Proofs’, Trans. AMS 177, 29–36.

    Google Scholar 

  • Pudlak, P.: forthcoming, ‘The Lengths of Proofs’, to appear in S. Buss (ed.), Handbook of Proof Theory, North Holland.

  • Statman, R.: 1981, ‘Speed-Up by Theories with Infinite Models’, Proc. Amer. Math. Soc. 81, 465–69.

    Google Scholar 

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Parikh, R. Length and Structure of Proofs. Synthese 114, 41–48 (1998). https://doi.org/10.1023/A:1005050425290

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