Journal of Symbolic Logic

Saturation and Σ₂-transfer for ERNA

Chris Impens

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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.

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

First available in Project Euclid: 16 June 2009

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

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