# Contradiction (inconsistency)

From Encyclopedia of Mathematics

A formula $\phi$ of the language of pure (or narrow) predicate calculus that is false in all models of this language. A formula $\phi$ is a contradiction if and only if $\neg\phi$ is derivable in pure predicate calculus.

**How to Cite This Entry:**

Contradiction (inconsistency).

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Contradiction_(inconsistency)&oldid=31391

This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article