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A '''counting quantifier''' is a [[Mathematics|mathematical]] term for a [[quantifier]] of the form "there exists at least ''k'' elements that satisfy property ''X''".
In [[first-order logic]] with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand.
However, they are interesting in the context of logics such as [[two-variable logic with counting]] that restrict the number of variables in formulas.
Also, generalized counting quantifiers that say "there exists infinitely many" are not expressible using a finite number of formulas in first-order logic.
==References==
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