The representation theorem of the Robinson hybrid

Abstract

This research lies within the domain of model theory, which investigates the properties of, broadly speaking, incomplete theories. The article introduces novel methods for classifying classes of structures whose associated theories are Jonssonian, forming a distinct subclass within the broader category of inductive theories. This subclass is characterized by satisfying the standard model-theoretic properties of joint embedding and amalgamation. The focus is placed specifically on the second kind of hybrids, those involving theories with different signatures. As a representative case of such hybrids among Jonsson theories, we examine the classical examples of the theory of unars and the theory of undirected graphs. The study proposes and formalizes several new notions, including the perfect Robinson hybrid, the center of a Robinson hybrid, the Kaiser class of a theory, and the concept of triple factorization. Within the framework of these definitions, we establish new results, among them a theorem confirming the existence of a unique countably categorical theory of S-acts, which is syntactically equivalent to the Robinson hybrid formed by the aforementioned classes.