Groundwork for weak analysis

Author:

Fernandes António M.,Ferreira Fernando

Abstract

AbstractThis 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference29 articles.

1. Buss Samuel , Bounded arithmetic, Ph.D. thesis , Princeton University, 06 1985, a revision of this thesis was published by Bibliopolis in 1986.

2. Friedman Harvey , FOM:73:Hilbert's program wide open?, FOM e-mail list: http://www.math.psu.edu/simpson/fom, 12 20 1999.

3. Metamathematics of First-Order Arithmetic

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