- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
An Effective Conservation Result for Nonstandard Arithmetic
Mathematical Logic Quarterly 46 (1):17-24 (2000)
Abstract
We prove that a nonstandard extension of arithmetic is effectively conservative over Peano arithmetic by using an internal version of a definable ultrapower. By the same method we show that a certain extension of the nonstandard theory with a saturation principle has the same proof-theoretic strength as second order arithmetic, where comprehension is restricted to arithmetical formulasOther Versions
No versions found
My notes
Similar books and articles
The strength of nonstandard methods in arithmetic.C. Ward Henson, Matt Kaufmann & H. Jerome Keisler - 1984 - Journal of Symbolic Logic 49 (4):1039-1058.
The strength of countable saturation.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2017 - Archive for Mathematical Logic 56 (5-6):699-711.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Transfer principles in nonstandard intuitionistic arithmetic.Jeremy Avigad & Jeremy Helzner - 2002 - Archive for Mathematical Logic 41 (6):581-602.
On certain types and models for arithmetic.Andreas Blass - 1974 - Journal of Symbolic Logic 39 (1):151-162.
Nonstandard second-order arithmetic and Riemannʼs mapping theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
Minimal models of Heyting arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
Definable sets and expansions of models of Peano arithmetic.Roman Murawski - 1988 - Archive for Mathematical Logic 27 (1):21-33.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Analytics
Added to PP
2013-12-01
Downloads
52 (#1,142,052)
6 months
4 (#1,748,177)
2013-12-01
Downloads
52 (#1,142,052)
6 months
4 (#1,748,177)
Historical graph of downloads
Citations of this work
A functional interpretation for nonstandard arithmetic.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2012 - Annals of Pure and Applied Logic 163 (12):1962-1994.
Non-principal ultrafilters, program extraction and higher-order reverse mathematics.Alexander P. Kreuzer - 2012 - Journal of Mathematical Logic 12 (1):1250002-.
References found in this work
A model for intuitionistic non-standard arithmetic.Ieke Moerdijk - 1995 - Annals of Pure and Applied Logic 73 (1):37-51.
Developments in constructive nonstandard analysis.Erik Palmgren - 1998 - Bulletin of Symbolic Logic 4 (3):233-272.
The strength of nonstandard methods in arithmetic.C. Ward Henson, Matt Kaufmann & H. Jerome Keisler - 1984 - Journal of Symbolic Logic 49 (4):1039-1058.
A constructive approach to nonstandard analysis.Erik Palmgren - 1995 - Annals of Pure and Applied Logic 73 (3):297-325.
A Predicative Approach to Nonstandard Mathematics.Peter Zahn - 1987 - Mathematical Logic Quarterly 33 (1):85-96.
Try MATCHA Writer if you're interested in citing directly from PhilPapers and certifying your authorship.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation