View source for Syntactic theorem

A theorem about a [[Syntactic language|syntactic language]] — that is, a theorem about a formal system —, such as a deduction theorem in predicate calculus, or Gödel's theorem on the incompleteness of arithmetic. These theorems are concerned with elementary syntax. An example of a non-elementary syntactic theorem — that is, a theorem whose proof essentially uses infinite sets — is the theorem on the consistency of elementary arithmetic.