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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
