ALGEBRAICALLY PRIME AND ATOMIC SETSA.R. YESHKEYEV, O.I. ULBRIKHT, A.K. ISSAYEVA (pp. 232-245)
Abstract.The main result of this work is related to the well-known problems which were appeared regarding a description of algebraically prime models. In this paper, the properties of algebraically prime and various types of atomic models are considered in the frame of the study of Jonsson theories. One of the important concepts of this article is a definable set with various additional properties that define the corresponding types of prime and atomic models. The defining formula of this set makes it possible to define the pregeometry on definable subsets of the semantic model of the considered Jonsson theory. Also was adapted for fixed Jonsson theories the existence of a prime model over a basic set.
Keywords:Jonsson theory, semantic model, prime model, atomic model, algebraically prime model, pregeometry, Jonsson set.