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Syntactic theorem

From Encyclopedia of Mathematics
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A theorem about a 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.

How to Cite This Entry:
Syntactic theorem. V.N. Grishin (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Syntactic_theorem&oldid=19055
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098