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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