Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T17:21:30.440Z Has data issue: false hasContentIssue false
  • English
  • Français

A feasible theory for analysis

Published online by Cambridge University Press:  12 March 2014

Fernando Ferreira
Fernando Ferreira*
Affiliation:
Universidade de Lisboa, Departamento de Matemática, 1700 Lisboa, Portugal, E-mail: mferferr@ptearn.bitnet
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 1001 - 1011
Copyright
Copyright © Association for Symbolic Logic 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[B85]Buss, S., Bounded arithmetic, Ph.D. Dissertation, Princeton University, Princeton, New Jersey, 1985, rev. version, Bibliopolis, Naples, 1986.Google Scholar
[B87]Buss, S., A conservation result concerning bounded theories and the collection axiom, Proceedings of the American Mathematical Society, vol. 100 (1987), pp. 709–715.CrossRefGoogle Scholar
[BS90]Buchholz, W. and Sieg, W., A note on polynomial time computable arithmetic, Contemporary Mathematics, vol. 106, American Mathematical Society, Providence, Rhode Island. 1990, pp. 51–55.Google Scholar
[F88]Ferreira, F., Polynomial time computable arithmetic and conservative extensions, Ph.D. Dissertation, Pennsylvania State University, University Park, Pennsylvania, 1988.Google Scholar
[F90]Ferreira, F., Polynomial time computable arithmetic, Contemporary Mathematics, vol. 106, American Mathematical Society, Providence, Rhode Island, 1990, pp. 137–156.Google Scholar
[Fta]Ferreira, F., A note on a result of Buss concerning bounded theories and the collection scheme, Portugaliae Mathematica (submitted).Google Scholar
[I89]Immerman, N., Descriptive and computational complexity, Computational complexity theory, Proceedings of Symposia in Applied Mathematics, vol. 38, American Mathematical Society, Providence, Rhode Island, 1989, pp. 75–91.CrossRefGoogle Scholar
[JS72]Jockusch, C. Jr. and Soare, R., classes and degrees of theories, Transactions of the American Mathematical Society, vol. 173 (1972), pp. 35–56.Google Scholar
[Sieg88]Sieg, W., Hilbert's Program sixty years later, this Journal, vol. 53 (1988), pp. 338–348.Google Scholar
[Sim87]Simpson, S., Subsystems of Z2 and reverse mathematics, Appendix to G. Takeuti, Proof theory, 2nd ed., North-Holland, Amsterdam, 1987, pp. 432–446.Google Scholar
[SS86]Simpson, S. and Smith, R., Factorization of polynomials and induction, Annals of Pure and Applied Logic, vol. 31 (1986), pp. 289–306.CrossRefGoogle Scholar