Infinite chains and antichains in computable partial orderings

Journal of Symbolic Logic 66 (2):923-934 (2001)
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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 antichain

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