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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.Links
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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.
Linear extensions of partial orders and reverse mathematics.Emanuele Frittaion & Alberto Marcone - 2012 - Mathematical Logic Quarterly 58 (6):417-423.
Reverse mathematics and initial intervals.Emanuele Frittaion & Alberto Marcone - 2014 - Annals of Pure and Applied Logic 165 (3):858-879.
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.
(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.
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.
Proof Theory and Logical Complexity.Helmut Pfeifer & Jean-Yves Girard - 1989 - Journal of Symbolic Logic 54 (4):1493.
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.
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