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A simple ordinal recursive normalization of Gödel's T

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Computer Science Logic (CSL 1997)

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References

  1. R. S. Boyer and J. S. Moore. A Computational Logic. Academic Press, 1979.

    Google Scholar 

  2. W. Buchholz: Notation systems for infinitary derivations. Archive for Mathematical Logic, (30) pp. 277–296, 1991.

    Google Scholar 

  3. J. Y. Girard: Proofs and types, Cambridge University Press, 1989

    Google Scholar 

  4. K. Gödel: Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Pp. 280–287, Dialectica 12 (1958).

    Google Scholar 

  5. A. Grzegorczyk: Some classes of recursive functions. Rozprawy Mate. No. IV, Warsaw 1953.

    Google Scholar 

  6. P. Hájek, P. Pudlák: Mathematics of first-order arithmetic. Springer Verlag 1993.

    Google Scholar 

  7. W. A. Howard: Assignment of ordinals to terms for primitive recursive functionals of finite type. In Intuitionism and Proof Theory, pp. 443–458, Amsterdamm 1970.

    Google Scholar 

  8. G. E. Mints: Finite investigations of transfinite derivations. Journal of Soviet Mathematics (10), pp. 548–596, 1978.

    Google Scholar 

  9. H. E. Rose: Subrecursion, Functions and Hierarchies. Clarendon Press, Oxford 1984.

    Google Scholar 

  10. J. R. Shoenfield: Mathematical logic. Addison Wesley, 1967.

    Google Scholar 

  11. K. Schütte: Proof Theory. Springer Verlag 1977.

    Google Scholar 

  12. H. Schwichtenberg: Elimination of higher type levels in definitions of primitive recursive functionals by means of transfinite recursion. In Logic Colloquium 1973 (eds. H. E. Rose and J. C. Shepherdson), North Holland, 1975.

    Google Scholar 

  13. H. Schwichtenberg: Classifying recursive functions. Handbook of Recursion Theory, to appear, 1996.

    Google Scholar 

  14. H. Schwichtenberg: Finite notations for infinite terms, to appear in APAL. Recursion Theory 96.

    Google Scholar 

  15. W. W. Tait: Nested recursion. Math. Ann. 143, pp. 236–250, 1961.

    Article  Google Scholar 

  16. W. W. Tait: Infinitely long terms of transfinite type. In Formal systems and recursive functions (ed. J. N. Crossley and M. Dummett), pp. 176–185, North Holland 1967.

    Google Scholar 

  17. P. J. Voda: Subrecursion as a basis for a feasible programming language. In L. Pacholski and J. Tiuryn, editors, Proceedings of CSL'94, number 933 in LNCS, pages 324–338. Springer Verlag, 1994.

    Google Scholar 

  18. A. Weiermann: A proof of strongly uniform termination for Gödel's T by methods from local predicativity, to appear in Archives for Math. Logic, 1997.

    Google Scholar 

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Mogens Nielsen Wolfgang Thomas

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© 1998 Springer-Verlag Berlin Heidelberg

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Voda, P.J. (1998). A simple ordinal recursive normalization of Gödel's T. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028033

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  • DOI: https://doi.org/10.1007/BFb0028033

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  • Online ISBN: 978-3-540-69353-6

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