Journal of Symbolic Logic

Groundwork for weak analysis

António M. Fernandes and Fernando Ferreira

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Abstract

This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, we show how to interpret the theory BTFA in Robinson’s theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q.

Article information

Source
J. Symbolic Logic, Volume 67, Issue 2 (2002), 557-578.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1190150098

Digital Object Identifier
doi:10.2178/jsl/1190150098

Mathematical Reviews number (MathSciNet)
MR1905155

Zentralblatt MATH identifier
1015.03056

Subjects
Primary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]

Citation

Fernandes, António M.; Ferreira, Fernando. Groundwork for weak analysis. J. Symbolic Logic 67 (2002), no. 2, 557--578. doi:10.2178/jsl/1190150098. https://projecteuclid.org/euclid.jsl/1190150098


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