Iota operator

The iota operator (also: labeling operator ) is predominantly used in linguistic-philosophical labeling theories that deal with the meaning of expressions of the form "der / die / das F". If these theories in (partial) formalized form, then use it as a description operator a small inverted 'J' or the Greek iota (hence the term iota operator ): The labeling

${\displaystyle \iota xF(x)}$

can be read as: "the x for which F (x) holds". It is a closed singular term that results from applying the operator to the in open formula . The identification operator links the free variable in . ${\displaystyle \iota x}$ ${\displaystyle {\mathit {x\,}}}$ ${\displaystyle F{\mathit {(x)\,}}}$ ${\displaystyle F{\mathit {(x)\,}}}$