Bulletin of Symbolic Logic 13 (1):54-70 (2007)

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 $I\Delta_0 + EXP$ , and on the other hand, $NQA^+$ interprets the theories IΣ1 and $WKL_0$
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DOI 10.2178/bsl/1174668218
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References found in this work BETA

Non-Standard Analysis.Gert Heinz Müller - 1969 - Journal of Symbolic Logic 34 (2):292-294.
An Overview of Interpretability Logic.Albert Visser - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 307-359.

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Citations of this work BETA

Transfer and a Supremum Principle for ERNA.Chris Impens & Sam Sanders - 2008 - Journal of Symbolic Logic 73 (2):689 - 710.
Erna and Friedman's Reverse Mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
More Infinity for a Better Finitism.Sam Sanders - 2010 - Annals of Pure and Applied Logic 161 (12):1525-1540.
Saturation and Σ₂-Transfer for ERNA.Chris Impens - 2009 - Journal of Symbolic Logic 74 (3):901-913.

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