On universal algebraic logic and cylindric algebras
Hajnal Andréka, Istvàn Németi · 1978
This is an abstract of the dissertation [1] which solved some problems raised in [2]. The subject is General Algebraic Logic in the sense of Rasiowa [5], but now for first order logics. Here we discuss the algebraic problems; their connections with (nonclassical and classical) logics were explained in [2]. The variety of cylindric algebras [4] was introduced for the classical first order logic; the present general algebraic (universal algebraic) approach is a generalization of the theory of that variety [4] to make it applicable to other first o. logics as well (cf. Freeman [6]). Throughout, α, β, γ denote infinite ordinals, ω is the set of natural numbers, and Ord is the class of in finite ordinals.