Groundwork for weak analysis

Journal of Symbolic Logic 67 (2):557-578 (2002)
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
On End‐Extensions of Models of ¬Exp.Fernando Ferreira - 1996 - Mathematical Logic Quarterly 42 (1):1-18.
Factorization of Polynomials and Σ10 Induction.Stephen G. Simpson & Rick L. Smith - 1986 - Annals of Pure and Applied Logic 31 (2):289-306.
Asymmetric Interpretations for Bounded Theories.Andrea Cantini - 1996 - Mathematical Logic Quarterly 42 (1):270-288.
Algebraic Disguises ofΣ 1 0 Induction.Kostas Hatzikiriakou - 1989 - Archive for Mathematical Logic 29 (1):47-51.

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Bounded Functional Interpretation and Feasible Analysis.Fernando Ferreira & Paulo Oliva - 2007 - Annals of Pure and Applied Logic 145 (2):115-129.

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