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Nonstandard Arithmetic and Reverse Mathematics

Published online by Cambridge University Press:  15 January 2014

H. Jerome Keisler
H. Jerome Keisler*
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA. E-mail: [email protected]
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Abstract

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 12 , Issue 1 , March 2006 , pp. 100 - 125
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

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