Note on a theorem of J. Folkman on transversals of infinite families with finitely many infinite members.
In: Journal of Combinatorial Theory - Series B, Vol. 30, No. 1: pp. 100-102
In this note we show by a simple direct proof that Folkman's necessary and sufficient condition for an infinite family of sets with finitely many infinite members to have a transversal implies Woodall's condition. A short proof of Folkman's theorem results by combining with Woodall's proof.