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Transfer and a supremum principle for ERNA

Published online by Cambridge University Press:  12 March 2014

Chris Impens  and
Sam Sanders
Chris Impens
Affiliation:
University of Ghent, Department of Pure Mathematics and Computer Algebra, Galglaan 2, B-9000 Gent, Belgium, E-mail: ci@cage.ugent.be, URL: http://cage.ugent.be/~ci
Sam Sanders
Affiliation:
University of Ghent, Department of Pure Mathematics and Computer Algebra, Galglaan 2, B-9000 Gent, Belgium, E-mail: sasander@cage.ugent.be, URL: http://cage.ugent.be/~sasander
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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 Πı-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a Σı-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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 689 - 710
Copyright
Copyright © Association for Symbolic Logic 2008

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