 It is used in the proof of Gödel's completeness theorem, among other places.The effective version of the lemma's statement, "every consistent computably enumerable theory can be extended to a complete consistent computably enumerable theory," fails (provided Peano Arithmetic is consistent) by Gödel's incompleteness theorem.The lemma was not published by Adolf Lindenbaum; it is originally attributed to him by Alfred Tarski.