  In his 1930 Ph.D. thesis, Gödel presented a complete axiomatization of first-order logic, based on the Principia Mathematica by Whitehead and Russell (Gödel 1930). Gödel proved his Completeness Theorem, namely that a formula is provable from the axioms if and only if it is valid. Gödel’s Completeness theorem was a step towards the resolution of Hilbert’s entscheidungsproblem.