Orthogonally complete algebraic system
type: Item
instance of: scholarly article
title: Orthogonally complete algebraic system
zbMATH Open document ID: 0767.03018
DOI: 10.1007/BF01978833
author: A. I. Omarov
published in: Algebra and Logic
publication date: 1993-06-29T00:00:00Z
review text: In studying a complete algebraic system over a complete atomless Boolean algebra it will be very useful to recall the concepts and methods of \textit{E. A. Palyutin} [Algebra Logika 19, 582-614 (1980; Zbl 0491.03011)], such as \(h\)-formulas, \(h\)-irreducibility, \(h\)-decomposability, and so on. In the present paper we will prove some properties of \(h\)-formulas and establish the Horn nature of the elementary theory of a complete algebraic system over a complete atomless Boolean algebra, from which follows a strengthening of the Main Theorem 5.14 of \textit{K. I. Bejdar} and \textit{A. V. Mikhalev}'s paper [Usp. Mat. Nauk 40, No. 6(246), 79-115 (1985; Zbl 0603.06003)]. In the second part of this paper we prove a theorem characterizing the saturation of a Boolean localization of an orthogonally complete algebraic system, which implies, in particular, Theorem 6.6 of Bejdar and Mikhaliev [loc. cit.].
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 08C10
zbMATH DE Number: 220165
zbMATH Keywords: \(h\)-formulas
zbMATH Keywords: complete algebraic system over a complete atomless Boolean algebra
zbMATH Keywords: elementary theory
zbMATH Keywords: saturation of a Boolean localization of an orthogonally complete algebraic system
MaRDI profile type: Publication
cites work: Orthogonal completeness and algebraic systems
cites work: For what filters is every reduced product saturated?
full work available at URL: https://doi.org/10.1007/bf01978833
OpenAlex ID: W2026283791
description: scientific article; zbMATH DE number 220165