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The Trade-Off Theorem and Fragments of Gödel’s T

  • Lars Kristiansen
  • Paul J. Voda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)

Abstract

In [3, 4] we study the functionals, functions and predicates of the system T − −. Roughly speaking, T − − is a version of Gödel’s T (see, for instance [1]) where the successor function cannot be used to define functionals, and a functional F is definable in T − − iff F is definable in Gödel’s T by a term t where no succesors occur in t (the numerical constant 1 might occur in t).

Keywords

Free Variable Exponential Term Successor Function Proof Theory Simple Iteration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Avigad, J., Feferman, S.: Gödel’s Functional (Dialectica) Interpretation. In: Buss, S. (ed.) Handbook of Proof Theory, Elsevier, Amsterdam (1998)Google Scholar
  2. Ershov, Y.L.: The model C of the Continuous Functionals. In: Logic colloquium 1976, North Holland, Amsterdam (1977)Google Scholar
  3. Kristiansen, L., Voda, P.J.: The Surprising Power of Restricted Programs and Goedel’s Functionals. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 345–358. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. Kristiansen, L., Voda, P.J.: Languages Capturing Complexity Classes. Nordic Journal of Computing 12, 89–115 (2005)MATHMathSciNetGoogle Scholar
  5. Kristiansen, L., Voda, P.J.: Characterizations of Functionals by Limits, Unpublished. Available from http://www.fmph.uniba.sk/~voda (Work in progress.)
  6. Kristiansen, L., Voda, P.J.: The Trade-off Theorem and Fragments of Gódel’s T. Unpublished. (A version of this paper containing most of the proofs.), Available from http://www.fmph.uniba.sk/~voda
  7. Normann, D., Palmgren, E., Stoltenberg-Hansen, V.: Hyperfinite Type Structures. Journal of Symbolic Logic 64, 1216–1242 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. Normann, D.: A Characterisation of the Continuous Functionals, Seminar note, URL: http://www.math.uio.no/~dnormann/Seminar.0803.pdf
  9. Shoenfield, J.: Mathematical Logic. Addison-Wesley, Reading (1967)MATHGoogle Scholar
  10. Schútte, K.: Proof Theory. Springer, Heidelberg (1977)Google Scholar
  11. Schwichtenberg, H.: Classifying Recursive Functions. In: Griffor, E.R. (ed.) Handbook of computability theory, Elsevier, Amsterdam (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lars Kristiansen
    • 1
    • 2
  • Paul J. Voda
    • 3
  1. 1.Faculty of EngineeringOslo University College 
  2. 2.Department of MathematicsUniversity of Oslo 
  3. 3.Institute of InformaticsComenius University Bratislava 

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