Groundwork for weak analysis

• Type: Article in International Scientific Journal
• Date: 2002

Authors

Fernandes, AA (Author) FEUP; Ferreira, F (Author) Other

Journal

Title: Journal of Symbolic Logic

Vol. 67

Pages: 557-578

ISSN: 0022-4812

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 13 Citations

Scopus - 13 Citations

Other information

Authenticus ID: P-000-P7N

DOI: 10.2178/jsl/1190150098

Abstract (EN): This paper develops the very basic notions of analysis in a beak second-order theory of arithmetic BTFA whose provably total function, 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 field, is interpretable in Q.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 22