"G\u00F6del's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. It makes a close link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proven in particular formal systems.It was first proved by Kurt G\u00F6del in 1929. It was then simplified in 1947, when Leon Henkin observed in his Ph.D."@en .