A counterexample to a conjecture of Scott and Suppes
W. W. Tait · Journal of Symbolic Logic · 1959
In [1], it is conjectured that if S is a sentence in the first-order functional calculus with identity, and every subsystem of every finite relational system which satisfies S also satisfies S, then S is finitely equivalent to a universal sentence. (Two sentences are finitely equivalent if and only if they are satisfied by the same finite relational systems.) The following sentence S refutes that conjecture, and moreover S is satisfied by all finite subsystems of all (finite or infinite) relational systems which satisfy it.1S contains as predicate letters only the two-place predicate letters ≦, R (and the identity symbol =).