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.
Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. IV
Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. I
Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. VI
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