The maximal linear extension theorem in second order arithmetic

DOI10.1007/s00153-011-0231-1zbMath1227.03076arXiv1009.1528OpenAlexW3098312506MaRDI QIDQ634769

Alberto Marcone, Richard A. Shore

Publication date: 16 August 2011

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1528

zbMATH Keywords

ATRmaximal chainMLEreverse mathematicswell-quasi-ordermaximal linear extensionMCwqo

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35)

Related Items

Reverse mathematics, well-quasi-orders, and Noetherian spaces ⋮ A computably enumerable partial ordering without computably enumerable maximal chains and antichains ⋮ Reverse mathematics and initial intervals ⋮ (EXTRA)ORDINARY EQUIVALENCES WITH THE ASCENDING/DESCENDING SEQUENCE PRINCIPLE ⋮ Computing maximal chains ⋮ The Reverse Mathematics of wqos and bqos ⋮ FINDING DESCENDING SEQUENCES THROUGH ILL-FOUNDED LINEAR ORDERS ⋮ Linear extensions of partial orders and reverse mathematics

Cites Work

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• Graph minors. XX: Wagner's conjecture
• Weak comparability of well orderings and reverse mathematics
• On Fraïssé's conjecture for linear orders of finite Hausdorff rank
• Reverse mathematics and ordinal exponentiation
• Theory of relations. Transl. from the French by P. Clote. With an appendix by Norbert Sauer.
• Ordered sets
• Computable linearizations of well-partial-orderings
• On Fraissé's order type conjecture
• The theory of well-quasi-ordering: a frequently discovered concept
• On the strength of Ramsey's theorem for pairs
• Combinatorial principles weaker than Ramsey's Theorem for pairs
• Ordinal numbers and the Hilbert basis theorem
• On Chains and Antichains in well Founded Partially Ordered Sets
• Program termination and well partial orderings
• Reverse mathematics and the equivalence of definitions for well and better quasi-orders
• Partially well ordered sets and partial ordinals
• Well-Quasi-Ordering, The Tree Theorem, and Vazsonyi's Conjecture
• Ordering by Divisibility in Abstract Algebras