Groundwork for weak analysis

Journal of Symbolic Logic 67 (2):557-578 (2002)

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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
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DOI 10.2178/jsl/1190150098
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
A Feasible Theory for Analysis.Fernando Ferreira - 1994 - Journal of Symbolic Logic 59 (3):1001-1011.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.

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Citations of this work BETA

Open Questions in Reverse Mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Bounded Functional Interpretation and Feasible Analysis.Fernando Ferreira & Paulo Oliva - 2007 - Annals of Pure and Applied Logic 145 (2):115-129.
Interpretability in Robinson's Q.Fernando Ferreira & Gilda Ferreira - 2013 - Bulletin of Symbolic Logic 19 (3):289-317.

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