In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields.
Contents 
In logic, semantic completeness is the converse of soundness for formal systems. A formal system is "semantically complete" when all tautologies are theorems whereas a formal system is "sound" when all theorems are tautologies. Kurt Gödel, Leon Henkin, and Emil Post all published proofs of completeness. (See History of the Church–Turing thesis.) A system is consistent if a proof never exists for both P and not P.
In mathematics, "complete" is a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion". See, for example, algebraically closed field or compactification.
