%0 Journal Article
%T Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. IV
%A Paolo Lipparini
%J Mathematics
%D 2008
%I arXiv
%X We extend to singular cardinals the model-theoretical relation $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in P. Lipparini, The compactness spectrum of abstract logics, large cardinals and combinatorial principles, Boll. Unione Matematica Italiana ser. VII, {\bf 4-B} 875--903 (1990). We extend some results obtained in Part II, finding equivalent conditions involving uniformity of ultrafilters and the existence of certain infinite matrices. Our present definition suggests a new compactness property for abstract logics.
%U http://arxiv.org/abs/0805.1548v1