Journal of Symbolic Logic 73 (2):689 - 710 (2008)

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a σ₁-supremum principle 'up-to-infinitesimals', and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is 'too strong' for finitism by reconsidering Rössler and Jeřábek's conclusions
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DOI 10.2178/jsl/1208359067
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References found in this work BETA

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Things That Can and Things That Cannot Be Done in PRA.Ulrich Kohlenbach - 2000 - Annals of Pure and Applied Logic 102 (3):223-245.

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Citations of this work BETA

Erna and Friedman's Reverse Mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
More Infinity for a Better Finitism.Sam Sanders - 2010 - Annals of Pure and Applied Logic 161 (12):1525-1540.
The Dirac Delta Function in Two Settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
Reverse-Engineering Reverse Mathematics.Sam Sanders - 2013 - Annals of Pure and Applied Logic 164 (5):528-541.

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