Archive for Mathematical Logic 46 (5-6):457-464 (2007)

Abstract
In their paper from 1981, Milner and Sauer conjectured that for any poset $\langle P,\le\rangle$ , if $cf(P,\le)=\lambda>cf(\lambda)=\kappa$ , then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ κ antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many well-known axioms such as GCH, SSH and PFA. The consistency of the negation of this hypothesis is unknown
Keywords Poset  Antichain  Singular cofinality
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DOI 10.1007/s00153-007-0049-z
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On the Consistency Strength of the Milner–Sauer Conjecture.Assaf Rinot - 2006 - Annals of Pure and Applied Logic 140 (1):110-119.
External Cofinalities and the Antichain Condition in Partial Orders.Isaac Gorelic - 2006 - Annals of Pure and Applied Logic 140 (1):104-109.

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