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On the length of proofs in a formal system of recursive arithmetic

  • Tohru Miyatake
Conference paper
  • 172 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 891)

Keywords

Inference Rule Free Variable Basic Sequent Main Lemma Remainder Function 
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References

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    Gentzen, G.: Investigations into logical deduction, in “The collected papers of G. Gentzen”, ed. by M. E. Szabo, North-Holland, 1969.Google Scholar
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    Goodstein, R.J.: Recusive number theory, Amsterdam, 1957.Google Scholar
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    Parikh, R.J.: Some results on the length of proofs, Trans. Amer. Math. Soc. 177 (1973), 29–36.MathSciNetCrossRefzbMATHGoogle Scholar
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    Rose, H.E.: On the consistency and undecidability of recursive arithmetic, Zeitschr. f. math. Logik u. Grundlagen d. Math., Bd. 7 S. 124–135, (1961).MathSciNetCrossRefzbMATHGoogle Scholar
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    Miyatake, T.: On the length of proofs in formal systems, Tsukuba J. Math. 4 (1980), 115–125.MathSciNetzbMATHGoogle Scholar
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    Yukami, T.: A theorem on the formalized arithmetic with function symbol ′ and +, Tsukuba J. Math. 1 (1977), 195–211.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1981

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  • Tohru Miyatake

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