- 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
The maximal linear extension theorem in second order arithmetic
Archive for Mathematical Logic 50 (5-6):543-564 (2011)
Abstract
We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.Other Versions
No versions found
Links
PhilArchive
External links
(no proxy)
Setup an account with your affiliations in order to access resources via your University's proxy server
Through your library
- Sign in / register and customize your OpenURL resolver
- Configure custom resolver
My notes
Similar books and articles
Maximal chains in the fundamental order.Steven Buechler - 1986 - Journal of Symbolic Logic 51 (2):323-326.
The independence of the prime ideal theorem from the order-extension principle.U. Felgner & J. K. Truss - 1999 - Journal of Symbolic Logic 64 (1):199-215.
Hindman's theorem: An ultrafilter argument in second order arithmetic.Henry Towsner - 2011 - Journal of Symbolic Logic 76 (1):353 - 360.
A model of peano arithmetic with no elementary end extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.
A theory for log-space and NLIN versus co-NLIN.Chris Pollett - 2003 - Journal of Symbolic Logic 68 (4):1082-1090.
Adding linear orders.Saharon Shelah & Pierre Simon - 2012 - Journal of Symbolic Logic 77 (2):717-725.
Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Analytics
Added to PP
2013-10-27
Downloads
196 (#206,075)
6 months
37 (#226,460)
2013-10-27
Downloads
196 (#206,075)
6 months
37 (#226,460)
Historical graph of downloads
Citations of this work
Finding descending sequences through ill-founded linear orders.Jun le Goh, Arno Pauly & Manlio Valenti - 2021 - Journal of Symbolic Logic 86 (2):817-854.
(Extra)Ordinary Equivalences with the Ascending/Descending Sequence Principle.Marta Fiori-Carones, Alberto Marcone, Paul Shafer & Giovanni Soldà - 2024 - Journal of Symbolic Logic 89 (1):262-307.
Reverse mathematics and initial intervals.Emanuele Frittaion & Alberto Marcone - 2014 - Annals of Pure and Applied Logic 165 (3):858-879.
Linear extensions of partial orders and reverse mathematics.Emanuele Frittaion & Alberto Marcone - 2012 - Mathematical Logic Quarterly 58 (6):417-423.
Reverse mathematics, well-quasi-orders, and Noetherian spaces.Emanuele Frittaion, Matthew Hendtlass, Alberto Marcone, Paul Shafer & Jeroen Van der Meeren - 2016 - Archive for Mathematical Logic 55 (3):431-459.
References found in this work
On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
Combinatorial principles weaker than Ramsey's Theorem for pairs.Denis R. Hirschfeldt & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (1):171-206.
Reverse mathematics and ordinal exponentiation.Jeffry L. Hirst - 1994 - Annals of Pure and Applied Logic 66 (1):1-18.
Weak comparability of well orderings and reverse mathematics.Harvey M. Friedman & Jeffry L. Hirst - 1990 - Annals of Pure and Applied Logic 47 (1):11-29.
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