Journal of Symbolic Logic

Saturation and Σ₂-transfer for ERNA

Chris Impens

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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.

Article information

Source
J. Symbolic Logic, Volume 74, Issue 3 (2009), 901-913.

Dates
First available in Project Euclid: 16 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1245158090

Digital Object Identifier
doi:10.2178/jsl/1245158090

Mathematical Reviews number (MathSciNet)
MR2548467

Zentralblatt MATH identifier
1184.03071

Citation

Impens, Chris. Saturation and Σ₂-transfer for ERNA. J. Symbolic Logic 74 (2009), no. 3, 901--913. doi:10.2178/jsl/1245158090. https://projecteuclid.org/euclid.jsl/1245158090


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