Language equations with all Boolean operations and concatenation and a particular order on the set of solutions are proved to be equal in expressive power to the first-order Peano arithmetic, In particular, it is shown that the class of sets representable using k variables (for every k ≥ 2) is exactly the k-th level of the arithmetical hierarchy, i.e., the sets definable by recursive predicates with k alternating quantifiers. The property of having an extremal solution is shown to be nonrepresentable in first-order arithmetic.