# Existential quantifier

From Encyclopedia of Mathematics

A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that" ). In formalized languages, existential quantifiers are denoted by $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$.

#### Comments

The *unique existential quantifier* forms the assertion that "there exists exactly one x such that" and is denoted $\exists!x$.

#### References

[a1] | A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974) |

[b1] | S.C. Kleene, "Mathematical Logic" repr. Dover (2013) ISBN 0486317072 |

**How to Cite This Entry:**

Existential quantifier.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Existential_quantifier&oldid=53845

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