Erna and Friedman's reverse mathematics

Journal of Symbolic Logic 76 (2):637 - 664 (2011)

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
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DOI 10.2178/jsl/1305810768
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References found in this work BETA

Nonstandard Arithmetic and Reverse Mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Transfer and a Supremum Principle for ERNA.Chris Impens & Sam Sanders - 2008 - Journal of Symbolic Logic 73 (2):689 - 710.

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Citations of this work BETA

The Dirac Delta Function in Two Settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
Reverse-Engineering Reverse Mathematics.Sam Sanders - 2013 - Annals of Pure and Applied Logic 164 (5):528-541.
On Algorithm and Robustness in a Non-Standard Sense.Sam Sanders - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao González, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 99--112.

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