1-ary functions and the f.c.p (Q752696)

A full classification of theories of 1-ary functions that do not satisfy the finite cover property is given. The proof uses the superstability of these theories, and the characterization of the finite cover property in terms of nice pairs; more precisely, the fact that if T is a stable theory then T does not satisfy the finite cover property if and only if every \(\omega_ 1\)-saturated model of the theory of nice pairs of models of T is a nice pair.