More infinity for a better finitism

Annals of Pure and Applied Logic 161 (12):1525-1540 (2010)
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Abstract

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed in around 1995 by Patrick Suppes and Richard Sommer. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes. Here, we discuss the inherent problems and limitations of the classical nonstandard framework and propose a much-needed refinement of ERNA, called , in the spirit of Karel Hrbacek’s stratified set theory. We study the metamathematics of and its extensions. In particular, we consider several transfer principles, both classical and ‘stratified’, which turn out to be related. Finally, we show that the resulting theory allows for a truly general, elegant and elementary treatment of basic analysis

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Sam Sanders
Ruhr-Universität Bochum

Citations of this work

Erna and Friedman's reverse mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
The Dirac delta function in two settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.
Is mathematical rigor necessary in physics?Kevin Davey - 2003 - British Journal for the Philosophy of Science 54 (3):439-463.

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