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Difference between revisions of "Contradiction (inconsistency)"

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A formula <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025900/c0259001.png" /> of the language of pure (or narrow) predicate calculus that is false in all models of this language. A formula <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025900/c0259002.png" /> is a contradiction if and only if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025900/c0259003.png" /> is derivable in pure predicate calculus.
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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.

Latest revision as of 14:11, 17 March 2014

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
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