## 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.