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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160749We extend to singular cardinals the model-theoretical relation $λ\stackrelκ{\Rightarrow} μ$ 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.10 pagesLogic03C20, 03E05, 03C95; 03C55, 03C98Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. IVtext