Abstract. We study properties of closure operators of singular cofinality, and introduce several ZFC sufficient and equivalent conditions for the existence of antichain sequences in posets of singular cofinality.
We also notice that the Proper Forcing Axiom implies the Milner-Sauer conjecture.
A. Rinot, Aspects of singular cofinality, Contrib. Discrete Math., 2(2): 185-204, 2007.