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Fragment of Nonstandard Analysis with a Finitary Consistency Proof

Published online by Cambridge University Press:  15 January 2014

Michal Rössler  and
Emil Jeřábek
Michal Rössler
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Prague, 115 67, Czech Republic, E-mail: [email protected]: [email protected]
Emil Jeřábek
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Prague, 115 67, Czech Republic, E-mail: [email protected]: [email protected]
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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.

Type
Communications
Information
Bulletin of Symbolic Logic , Volume 13 , Issue 1 , March 2007 , pp. 54 - 70
Copyright
Copyright © Association for Symbolic Logic 2007

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