Finite models are one-generated

Every finite model is definitionally equivalent to a model with a single relation and, although on a fixed non-empty finite set there are infinitely many different relations (the arity of a relation may be arbitrarily large), the number of definitionally non-equivalent finite models with the same universe is finite. In cylindric algebraic terms, the result is the infinite dimensional counterpart of the result proved by S. Comer, H. Andréka and I. Németi according to which any n-dimensional cylindric set algebra with base of power < n+2 can be generated by a single element, if n is finite.