Existential quantifier

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[edit]

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

#### References[edit]

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

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