An operator $\epsilon$ serving to formalize the notion of an indefinite description in predicate logic introduced by mathematicians David Hilbert (1862–1943) and Paul Bernays (1888–1977). When $\epsilon$ is taken as primitive, $\epsilon$ takes a formula $\phi \left(x\right)$ and produces an expression $\epsilon x.\phi \left(x\right)$. This expression is taken to refer to an arbitrarily chosen individual of a domain that satisfies the formula $\phi \left(x\right)$, so long as there exists such an individual. As an illustration, where a formula $Lx$ is interpreted as the predicate ‘$x$ is a lion’, the term $\epsilon x.Lx$ corresponds to the expression ‘a lion’. Hilbert and Bernays’ extension of classical predicate logic by $\epsilon$ terms—known as the epsilon calculus—recursively constructs complex formulae in which phrases of the form $\epsilon x.\phi \left(x\right)$ play the role of terms. This yields formulae such as $\psi \left(\epsilon x.\phi \left(x\right)\right)$, read as ‘something satisfying $\phi \left(x\right)$ also satisfies $\psi \left(x\right)$’. Furthermore, the classical existential and universal quantifiers can be defined from $\epsilon$, by, e.g., identifying an existentially quantified formula $\exists x\phi \left(x\right)$ with the quantifier-free formula $\phi \left(\epsilon x.\phi \left(x\right)\right)$.