Journal of Symbolic Logic

Groundwork for weak analysis

António M. Fernandes and Fernando Ferreira

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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

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

First available in Project Euclid: 18 September 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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