Normality of Horn theories with a nonmaximal spectrum (Q1086227)

The main result of this article is the following. If a Horn theory T (not necessarily complete) has a nonmaximal uncountable spectrum, then it is normal. This result is a corollary to the following theorem: If T is a complete theory whose h-companion \(T^ h\) is superstable and does not have the dimension order property (dop), then each formula T is equivalent to a Boolean combination of h-formulas and formulas having no more than one free variable. These results are used for estimating the spectrum of the h-companion and describing uncountable spectra of arbitrary (not complete) Horn classes, in particular, quasivarieties.