 In 1930 Gödel published the paper based on his thesis (Gödel 1930) notable also for the inclusion of the compactness theorem, which is only implicitly stated in the thesis. The theorem as stated by Gödel in Gödel 1930 is as follows: a countably infinite set of quantificational formulas is satisfiable if and only if every finite subset of those formulas is satisfiable. Gödel uses compactness to derive a generalization of the completeness theorem.