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Saturation and Σ2-transfer 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
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
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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 around 1995 by Patrick Suppes and Richard Sommer. It is built on a previous system by Rolando Chuaqui and Patrick Suppes, which was recently reconsidered by Michal Rössler and Emil Jeřábek. A Π1-transfer principle has already been added to ERNA and the consistency of the resulting theory proved in PRA. Here, we equip ERNA with Σ2-transfer and a saturation principle, while keeping the consistency proof inside PRA. We show that the extended theory allows for generalized transfer, a basic tool of nonstandard analysis, and interprets several strong theories, like BΣ2 and IΣ2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 901 - 913
Copyright
Copyright © Association for Symbolic Logic 2009

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