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June 2008 Transfer and a supremum principle for ERNA
Chris Impens, Sam Sanders
J. Symbolic Logic 73(2): 689-710 (June 2008). DOI: 10.2178/jsl/1208359067

Abstract

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.

Citation

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Chris Impens. Sam Sanders. "Transfer and a supremum principle for ERNA." J. Symbolic Logic 73 (2) 689 - 710, June 2008. https://doi.org/10.2178/jsl/1208359067

Information

Published: June 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1141.03032
MathSciNet: MR2414472
Digital Object Identifier: 10.2178/jsl/1208359067

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 2 • June 2008
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