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Infinite chains and antichains in computable partial orderings
Journal of Symbolic Logic 66 (2):923-934 (2001)
Abstract
We show that every infinite computable partial ordering has either an infinite Δ 0 2 chain or an infinite Π 0 2 antichain. Our main result is that this cannot be improved: We construct an infinite computable partial ordering that has neither an infinite Δ 0 2 chain nor an infinite Δ 0 2 antichainLinks
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Citations of this work
Reverse mathematics and the equivalence of definitions for well and better quasi-orders.Peter Cholak, Alberto Marcone & Reed Solomon - 2004 - Journal of Symbolic Logic 69 (3):683-712.
Self-Embeddings of Computable Trees.Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, James H. Schmerl & Reed Solomon - 2008 - Notre Dame Journal of Formal Logic 49 (1):1-37.
Chains and antichains in partial orderings.Valentina S. Harizanov, Carl G. Jockusch & Julia F. Knight - 2009 - Archive for Mathematical Logic 48 (1):39-53.
Preface.Douglas Cenzer, Valentina Harizanov, David Marker & Carol Wood - 2009 - Archive for Mathematical Logic 48 (1):1-6.
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