Two forms of Completeness Theorem Let Γ be a set of wffs. The following parts are equivalent. If Γ |= A then Γ ` A If Γ is consistent, then Γ is satisfiable
The need for a richer language In P, it is not possible to express assertions about elements of a structure. First Order Logic is a considerably richer logic than propositional logic, but yet enjoys many nice mathematical properties