Combinatorial and model-theoretical principles related to regularity of   ultrafilters and compactness of topological spaces. II
  We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1].   Our conditions involve uniformity of ultrafilters, compactness properties of products of topological spaces and the existence of certain infinite matrices. 
Paolo Lipparini