Annals of Pure and Applied Logic 59 (1):33-43 (1993)

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
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DOI 10.1016/0168-0072(93)90229-7
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Omitting Uncountable Types and the Strength of [0,1]-Valued Logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.
Cauchy Completeness in Elementary Logic.J. C. Cifuentes, A. M. Sette & D. Mundici - 1996 - Journal of Symbolic Logic 61 (4):1153-1157.
XI Latin American Symposium on Mathematical Logic.Carlos Augusto Di Prisco - 1999 - Bulletin of Symbolic Logic 5 (4):495-524.

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