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The strength of nonstandard methods in arithmetic

Published online by Cambridge University Press:  12 March 2014

C. Ward Henson ,
Matt Kaufmann  and
H. Jerome Keisler
C. Ward Henson
Affiliation:
University of Illinois, Urbana, Illinois 61801
Matt Kaufmann
Affiliation:
Purdue University, West Lafayette, Indiana 47907
H. Jerome Keisler
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706
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Abstract

We consider extensions of Peano arithmetic suitable for doing some of nonstandard analysis, in which there is a predicate N(x) for an elementary initial segment, along with axiom schemes approximating ω1-saturation. We prove that such systems have the same proof-theoretic strength as their natural analogues in second order arithmetic. We close by presenting an even stronger extension of Peano arithmetic, which is equivalent to ZF for arithmetic statements.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 4 , December 1984 , pp. 1039 - 1058
Copyright
Copyright © Association for Symbolic Logic 1984

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References

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