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Formalizing non-standard arguments in second-order arithmetic

Published online by Cambridge University Press:  12 March 2014

Keita Yokoyama
Keita Yokoyama*
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. E-mail: y-keita@math.tohoku.ac.jp
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Abstract

In this paper, we introduce the systems ns-ACA0 and ns-WKL0 of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA0 and WKL0, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA0 or ns-WKL0 into proofs in ACA0 or WKL0.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1199 - 1210
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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