Logical quantifiers

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Logical quantifiers are used in first order logic and in logic of higher order.

Existential quantifier

The existential quantifier, i.e. there exists at least one, is denoted with the inverted latin character $\mathrm{\exists }$.

Uniqueness quantifier

The uniqueness quantifier, i.e. there exists one and only one, is denoted with $\mathrm{\exists }!$.

Example:

$\mathrm{\exists }!p\in \mathbb{\mathbb{N}}:p\text{ prime and }p\text{ even}.$

Universal quantifier

The universal quantifier, i.e. for all, is denoted with the inverted latin character $\mathrm{\forall }$.