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Models of superstable Horn theories. (English. Russian original) Zbl 0597.03017
Algebra Logic 24, 171-210 (1985); translation from Algebra Logika 24, No. 3, 278-326 (1985).
The main aim of this paper is the development of a structural theory for models of complete Horn theories with non-maximal spectra. A termal lemma, proved in the paper, permits to prove the existence of a prime model over any independent set of models of a complete Horn theory with non-maximal spectrum. It is proved that any model may be decomposed into submodels of smaller depths. This gives the possibility to characterize models of Horn theories with non-maximal spectra. Lower and upper bounds of the spectra of complete Horn theories are found. This gives a proximate characterization of the spectrum of a complete Horn theory if its depth is 1 or \(>\omega\).
Reviewer: S.R.Kogalovskij

MSC:
03C45 Classification theory, stability and related concepts in model theory
03C35 Categoricity and completeness of theories
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