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 $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$.
The unique existential quantifier forms the assertion that "there exists exactly one x such that" and is denoted $\exists!x$.
|[a1]||A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974)|
|[b1]||S.C. Kleene, "Mathematical Logic" repr. Dover (2013) ISBN 0486317072|
Existential quantifier. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Existential_quantifier&oldid=53845