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

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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

  1. Chang, C.C. & Keisler, H.J.: Model Theory, North-Holland, Amsterdam, 1973.

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  2. Curry, H.B.: A formalization of recursive arithmetic, Amer. J. Math. 63 (1941), 263–282.

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  3. Cleave, J.P. & Rose, H.E.: n-arithmetic, in “Sets, models and recursion theory” ed. by Crossley, North-Holland, Amsterdam, 1967.

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  4. Gentzen, G.: Investigations into logical deduction, in “The collected papers of G. Gentzen”, ed. by M. E. Szabo, North-Holland, 1969.

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  5. Goodstein, R.J.: Recusive number theory, Amsterdam, 1957.

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  6. Parikh, R.J.: Some results on the length of proofs, Trans. Amer. Math. Soc. 177 (1973), 29–36.

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  7. 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).

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  8. Miyatake, T.: On the length of proofs in formal systems, Tsukuba J. Math. 4 (1980), 115–125.

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  9. Yukami, T.: A theorem on the formalized arithmetic with function symbol ′ and +, Tsukuba J. Math. 1 (1977), 195–211.

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© 1981 Springer-Verlag

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Miyatake, T. (1981). On the length of proofs in a formal system of recursive arithmetic. In: Müller, G.H., Takeuti, G., Tugué, T. (eds) Logic Symposia Hakone 1979, 1980. Lecture Notes in Mathematics, vol 891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090981

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  • DOI: https://doi.org/10.1007/BFb0090981

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11161-0

  • Online ISBN: 978-3-540-38633-9

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