Journal of Symbolic Logic 73 (2):689 - 710 (2008)

Abstract
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a σ₁-supremum principle 'up-to-infinitesimals', and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is 'too strong' for finitism by reconsidering Rössler and Jeřábek's conclusions
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1208359067
Options
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: 56,060
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Things That Can and Things That Cannot Be Done in PRA.Ulrich Kohlenbach - 2000 - Annals of Pure and Applied Logic 102 (3):223-245.

Add more references

Citations of this work BETA

Erna and Friedman's Reverse Mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
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.

View all 6 citations / Add more citations

Similar books and articles

Saturation and Σ₂-Transfer for ERNA.Chris Impens - 2009 - Journal of Symbolic Logic 74 (3):901-913.
Two Objections to Yaffe on the Criminalization of Attempts.Alexander Sarch - 2014 - Criminal Law and Philosophy 8 (3):569-587.
9 The Transfer of Nonresponsibility.John Martin Fischer - 2004 - In Joseph K. Campbell (ed.), Freedom and Determinism. Cambridge Ma: Bradford Book/Mit Press.
Why Punish Attempts at All? Yaffe on 'The Transfer Principle'.Douglas Husak - 2012 - Criminal Law and Philosophy 6 (3):399-410.
Enabling Relations As a Way to Transfer Causal Sufficiency.Manuel Liz Gutiérrez - 2007 - The Proceedings of the Twenty-First World Congress of Philosophy 5:87-93.
Incompatibilism and the Logic of Transfer.Danilo šuster - 2004 - Acta Analytica 19 (33):45-54.
The Transfer Principle.Yoshindo Suzuki - 1985 - British Journal for the Philosophy of Science 36 (1):61-66.
Explaining Information Transfer in Quantum Teleportation.Armond Duwell - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S288-.
A Transfer Principle in Harmonic Analysis.Gaisi Takeuti - 1979 - Journal of Symbolic Logic 44 (3):417-440.
Transfer Principle in Quantum Set Theory.Masanao Ozawa - 2007 - Journal of Symbolic Logic 72 (2):625 - 648.
Mechanisms of Knowledge Transfer.Timothy J. Nokes - 2009 - Thinking and Reasoning 15 (1):1 – 36.

Analytics

Added to PP index
2010-08-24

Total views
22 ( #468,194 of 2,403,826 )

Recent downloads (6 months)
1 ( #550,507 of 2,403,826 )

How can I increase my downloads?

Downloads

My notes