Lindenbaum's lemma
In mathematical logic, Lindenbaum's lemma states that any consistent theory of predicate logic can be extended to a complete consistent theory. The lemma is a special case of the ultrafilter lemma for Boolean algebras, applied to the Lindenbaum algebra of a theory.Uses
It is used in the proof of Gödel's completeness theorem, among other places.Extensions
The effective version of the lemma's statement, "every consistent computably enumerable theory can be extended to a complete consistent computably enumerable theory," fails by Gödel's incompleteness theorem.History
The lemma was not published by Adolf Lindenbaum; it is originally attributed to him by Alfred Tarski.
