Journal of Symbolic Logic 74 (3):901-913 (2009)

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. It is built on a previous system by Rolando Chuaqui and Patrick Suppes, which was recently reconsidered by Michal Rössler and Emil Jeřábek. A $\Pi _1 $ -transfer principle has already been added to ERNA and the consistency of the resulting theory proved in PRA. Here, we equip ERNA with Σ₂-transfer and a saturation principle, while keeping the consistency proof inside PRA. We show that the extended theory allows for generalized transfer, a basic tool of nonstandard analysis, and interprets several strong theories, like BΣ₂ and IΣ₂
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1245158090
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,480
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

More Infinity for a Better Finitism.Sam Sanders - 2010 - Annals of Pure and Applied Logic 161 (12):1525-1540.
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.

Add more citations

Similar books and articles

Transfer and a Supremum Principle for ERNA.Chris Impens & Sam Sanders - 2008 - Journal of Symbolic Logic 73 (2):689 - 710.
Pseudo-Finite Homogeneity and Saturation.Jörg Flum & Martin Ziegler - 1999 - Journal of Symbolic Logic 64 (4):1689-1699.
Explaining Information Transfer in Quantum Teleportation.Armond Duwell - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S288-.
Saturated Models of Peano Arithmetic.J. F. Pabion - 1982 - Journal of Symbolic Logic 47 (3):625-637.
Accessible Categories, Saturation and Categoricity.Jiří Rosický - 1997 - Journal of Symbolic Logic 62 (3):891-901.
Mechanisms of Knowledge Transfer.Timothy J. Nokes - 2009 - Thinking and Reasoning 15 (1):1 – 36.
Window on Eastern Europe.Katrin Erna Hjort - 1996 - Business Ethics 5 (3):171-177.
Recent Discussion of Subjunctive Conditionals.Erna F. Schneider - 1953 - Review of Metaphysics 6 (4):623 - 649.


Added to PP index

Total views
6 ( #1,029,226 of 2,330,638 )

Recent downloads (6 months)
2 ( #394,426 of 2,330,638 )

How can I increase my downloads?


My notes