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Fragment of Nonstandard Analysis with a Finitary Consistency Proof
Published online by Cambridge University Press: 15 January 2014
Abstract
We introduce a nonstandard arithmetic NQA− based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by NQA+), with a weakened external open minimization schema. A finitary consistency proof for NQA− formalizable in PRA is presented. We also show interesting facts about the strength of the theories NQA−and NQA+; NQA−is mutually interpretable with IΔ0 + EXP, and on the other hand, NQA+interprets the theories IΣ1 and WKL0.
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