Definition
A topological space is said to be super countably paracompact iff. for every decreasing sequence of closed sets with an empty intersection, there is a decreasing sequence of cozero sets with and have an empty intersection.
Reference
John J. Schommer and Mary Anne Swardson, Almost realcompactness, Commentationes Mathematicae Universitatis Carolinae, Vol. 42 (2001), No. 2, 383–392.