Abstract
In classical model theory two objects of different nature correspond to every signature σ:L -the first-order language of σ and K -the class of all structures of σ.But there is a well-known one-to-one correspondence between maximal consistent sets of sentences of L and minimal axiomatizable classes in L of structures from K. When we say that we study the complete theory T we usually mean the pair (Γ,Mod(T)), where Mod(T) is the class of all models of T. In connection with this duality of the nature of complete theories I want to introduce two notions of similarity which play the role of isomorphisms and two notions of nearness of theories.§1.Syntactical similarity.Let F n (T), n < ω, be the Boolean algebras of formulas of T with exactly n free variables υi, . . ., v n , and F(T) = \J n F n (T).