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ERNA and Friedman's Reverse Mathematics

Published online by Cambridge University Press:  12 March 2014

Sam Sanders
Sam Sanders*
Affiliation:
University of Ghent, Department of Mathematics, Krijgslaan 281, B-9000 Gent, Belgium, E-mail: [email protected]
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Abstract

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. Recently, the author showed the consistency of ERNA with several transfer principles and proved results of nonstandard analysis in the resulting theories (see [12] and [13]). Here, we show that Weak König's lemma (WKL) and many of its equivalent formulations over RCA0 from Reverse Mathematics (see [21] and [22]) can be ‘pushed down’ into the weak theory ERNA, while preserving the equivalences, but at the price of replacing equality with equality ‘up to infinitesimals’. It turns out that ERNA plays the role of RCA0 and that transfer for universal formulas corresponds to WKL.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 637 - 664
Copyright
Copyright © Association for Symbolic Logic 2011

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