Orthogonally complete algebraic system
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.].
complete algebraic system over a complete atomless Boolean algebra
saturation of a Boolean localization of an orthogonally complete algebraic system
scientific article; zbMATH DE number 220165