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).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Avigad, J., Feferman, S.: Gödel’s Functional (Dialectica) Interpretation. In: Buss, S. (ed.) Handbook of Proof Theory, Elsevier, Amsterdam (1998)
Ershov, Y.L.: The model C of the Continuous Functionals. In: Logic colloquium 1976, North Holland, Amsterdam (1977)
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)
Kristiansen, L., Voda, P.J.: Languages Capturing Complexity Classes. Nordic Journal of Computing 12, 89–115 (2005)
Kristiansen, L., Voda, P.J.: Characterizations of Functionals by Limits, Unpublished. Available from http://www.fmph.uniba.sk/~voda (Work in progress.)
Kristiansen, L., Voda, P.J.: The Trade-off Theorem and Fragments of Gódel’s T. Unpublished.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
Normann, D., Palmgren, E., Stoltenberg-Hansen, V.: Hyperfinite Type Structures. Journal of Symbolic Logic 64, 1216–1242 (1999)
Normann, D.: A Characterisation of the Continuous Functionals, Seminar note, URL: http://www.math.uio.no/~dnormann/Seminar.0803.pdf
Shoenfield, J.: Mathematical Logic. Addison-Wesley, Reading (1967)
Schútte, K.: Proof Theory. Springer, Heidelberg (1977)
Schwichtenberg, H.: Classifying Recursive Functions. In: Griffor, E.R. (ed.) Handbook of computability theory, Elsevier, Amsterdam (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kristiansen, L., Voda, P.J. (2006). The Trade-Off Theorem and Fragments of Gödel’s T . In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_62
Download citation
DOI: https://doi.org/10.1007/11750321_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
eBook Packages: Computer ScienceComputer Science (R0)