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June 2002 Groundwork for weak analysis
António M. Fernandes, Fernando Ferreira
J. Symbolic Logic 67(2): 557-578 (June 2002). DOI: 10.2178/jsl/1190150098

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.

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António M. Fernandes. Fernando Ferreira. "Groundwork for weak analysis." J. Symbolic Logic 67 (2) 557 - 578, June 2002. https://doi.org/10.2178/jsl/1190150098

Information

Published: June 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1015.03056
MathSciNet: MR1905155
Digital Object Identifier: 10.2178/jsl/1190150098

Subjects:
Primary: 03F35
Secondary: 03B30

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.67 • No. 2 • June 2002
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