Milner–Sauer conjecture on antichains in posets of singular cofinality
Milner–Sauer conjecture. If cf(P,≤)=λ>cf(λ)=κ\operatorname{cf}(P,\le)=\lambda>\operatorname{cf}(\lambda)=\kappacf(P,≤)=λ>cf(λ)=κ, then PPP contains an antichain of size κ\kappaκ.