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

2008/05/11 by Lipparini, Paolo
#03C20 #03C55 #03C95 #03C98 #03E05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0805.1548

Abstract

We extend to singular cardinals the model-theoretical relation λ\stackrelκ⇒ 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.

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