Combinatorial and model-theoretical principles related to regularity of   ultrafilters and compactness of topological spaces. III
  We generalize the results from "P. Lipparini, Productive $[\lambda,\mu]$-compactness and regular ultrafilters, Topology Proceedings, 21 (1996), 161--171"; in particular the present results apply to singular cardinals, too. 
Paolo Lipparini