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

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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DOI 10.1016/j.apal.2010.06.003
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References found in this work BETA

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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