Journal of Symbolic Logic

ERNA and Friedman's Reverse Mathematics

Sam Sanders

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 2 (2011), 637-664.

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1305810768

Digital Object Identifier
doi:10.2178/jsl/1305810768

Mathematical Reviews number (MathSciNet)
MR2830420

Zentralblatt MATH identifier
1231.03059

Citation

Sanders, Sam. ERNA and Friedman's Reverse Mathematics. J. Symbolic Logic 76 (2011), no. 2, 637--664. doi:10.2178/jsl/1305810768. https://projecteuclid.org/euclid.jsl/1305810768


Export citation