that any sentence that is provable from a (possibly empty) set of premises/sentences is also a semantic consequence of that set, i.e., is true in any model that makes all members of . Symbolically we write, if , then . Notice that when is empty, we have the statement of weak soundness.

Arithmetic soundness

If T is a theory whose objects of discourse can be interpreted as natural numbers, we say T is arithmetically sound if

1.Previous
3.Next