Antichains in partially ordered sets of singular cofinality |
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Authors: | Assaf Rinot |
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Affiliation: | (1) School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel |
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Abstract: | In their paper from 1981, Milner and Sauer conjectured that for any poset , if , 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. |
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Keywords: | Poset Antichain Singular cofinality |
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