Some progress on the Aharoni-Korman conjecture (Q1613436)

\textit{R. Aharoni} and \textit{V. Korman} [Order 9, 245-253 (1992; Zbl 0766.06004)] have conjectured that every ordered set without infinite antichains possesses a chain and a partition into antichains so that each part intersects the chain. Related to both Aharoni's extension of the König duality theorem and Dilworth's theorem, this is an important conjecture in the theory of infinite orders. It is verified for ordered sets of the form \(C\times P\), where \(C\) is a chain and \(P\) is finite, and for ordered sets with no infinite antichains and no infinite intervals.