Abstract

We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model spaces of L are not normal for vocabularies of uncountable power ωα. It also follows that first-order logic is the only finite-dependence logic having normal model spaces and satisfying at the same time the downward Löwenheim-Skolem theorem and uniform reduction for pairs