Any statement which is not logically valid (read: always true) is unprovable. The statement ∃x∃y(x>y) is not provable from the theory of linear orders, since i

Any statement which is not logically valid (read: always true) is unprovable. The statement ∃x∃y(x>y) is not provable from the theory of linear orders, since it is false in the singleton order. On the other hand, it is not disprovable since any other order type would satisfy it. The statement ∃x(x2−2=0) is not provable from the axioms of the field, since Q thinks this is false, and C thinks it is true.