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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: [email protected]
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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

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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