Categorical Horn classes. II
type: Item
instance of: scholarly article
title: Categorical Horn classes. II
zbMATH Open document ID: 1220.03013
published in: Algebra and Logic
publication date: 2011-06-08T00:00:00Z
review text: A class of structures is called a Horn class if it is axiomatizable and closed under taking reduced products. The paper under review is a continuation of Part I, published a long time ago [Algebra Logic 19, 377--400 (1981); translation from Algebra Logika 19, 582--614 (1980; Zbl 0491.03011)]. A characterization of uncountably categorical Horn classes is obtained which implies that the classes in question have the property of being model-complete. There are also the following results: quantifier elimination down to primitive formulas, a description of groups interpretable in models of categorical Horn theories, and a description of groups interpretable in models of almost strongly minimal Horn theories. The author proves (contrary to his intention claimed in the paper mentioned above) that there exists a categorical Horn class of structures which cannot be extended to an almost strongly minimal primitive normal class, and to a categorical quasivariety in particular.
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C48
zbMATH DE Number: 5905265
zbMATH Keywords: categorical Horn classes
zbMATH Keywords: model completeness, quantifier elimination down to primitive formulas
zbMATH Keywords: interpretability
author: E. A. Palyutin
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
full work available at URL: s10469-011-9115-z
OpenAlex ID: W2152550326
cites work: Q4081299
cites work: Q3792668
cites work: Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory
cites work: Q4700633
cites work: Q4517146
DOI: 10.1007/S10469-011-9115-Z
description: scientific article; zbMATH DE number 5905265