Abstract

Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$ , where F is finite and I 1 , I 2 ,...,I n are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite relational language are also mentioned