The number of the models of complete Horn theories of finite depth
type: Item
instance of: scholarly article
title: The number of the models of complete Horn theories of finite depth
zbMATH Open document ID: 0638.03031
DOI: 10.1007/BF01988802
published in: Algebra and Logic
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187354
review text: Let T be an elementary theory. The spectrum of T is the cardinal function \(J_ T\) that associates with each cardinal \(\omega_{\alpha}\) the number of nonisomorphic T-models of cardinality \(\omega_{\alpha}\). \(J_ T\) is called a maximal spectrum if \(J_ T(\omega_{\alpha})=2^{\omega_{\alpha}}\) for \(\alpha\geq 1\). Developing ideas of S. Shelah, \textit{J. Saffe} [Ann. Pure Appl. Logic 24, 231-261 (1983; Zbl 0518.03010)] had given a complete description of the spectra of \(\omega\)-stable theories. The results of \textit{J. Saffe, E. A. Palyutin} and \textit{S. S. Starchenko} [Algebra Logika 24, No.3, 278-326 (1985; Zbl 0597.03017)] reduced the problem of describing the spectra for complete (countable) Horn theories to the problem of describing the nonmaximal spectra for complete Horn theories of finite depth. In the present paper, this last problem is solved.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 4039869
zbMATH Keywords: nonmaximal spectra
zbMATH Keywords: complete Horn theories of finite depth
author: S. Starchenko
MaRDI profile type: Publication
cites work: Varieties of logical matrices
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cites work: Q3931364
OpenAlex ID: W2069299647
description: scientific article; zbMATH DE number 4039869