JUCS - Journal of Universal Computer Science 14(6): 908-937, doi: 10.3217/jucs-014-06-0908
The Riemann Integral in Weak Systems of Analysis
expand article infoFernando Ferreira‡, Gilda Ferreira§
‡ Universidade de Lisboa, Lisboa, Portugal§ CMAF-Universidade de Lisboa, Lisboa, Portugal

Corresponding author: Fernando Ferreira ( ferferr@cii.fc.ul.pt )

© Fernando Ferreira, Gilda Ferreira.
This article is freely available under the J.UCS Open Content License.
Citation: Ferreira F, Ferreira G (2008) The Riemann Integral in Weak Systems of Analysis. JUCS - Journal of Universal Computer Science 14(6): 908-937. https://doi.org/10.3217/jucs-014-06-0908
Open Access
Abstract
Taking as a starting point (a modification of) a weak theory of arithmetic of Jan Johannsen and Chris Pollett (connected with the hierarchy of counting functions), we introduce successively stronger theories of bounded arithmetic in order to set up a system for analysis (TCA2). The extended theories preserve the connection with the counting hierarchy in the sense that the algorithms which the systems prove to halt are exactly the ones in the hierarchy. We show that TCA2 has the exact strength to develop Riemannian integration for functions with a modulus of uniform continuity.
Keywords
weak analysis, Riemann integral, counting hierarchy