A model $\mathfrak{𝔐}$ of a deductive system with quantifiers in which there exists a constant for each element in the domain $M$ of $\mathfrak{M}$. When a model $\mathfrak{M}$ is not a Henkin model, one may generally still construct a corresponding Henkin model $\left(\mathfrak{M},M\right)$ by adding to the signature of $\mathfrak{M}$ a constant $\underset{\_}{a}$ for each $a\in M$ where the interpretation of $\underset{\_}{a}$ in $\left(\mathfrak{M},M\right)$ is $a$ itself. The semantics for quantifiers frequently explicitly or implicitly appeal to corresponding Henkin models, as illustrated by definitions such as the following classical definition for the universal quantifier:

$\mathfrak{M}\models \forall x\phi \left(x\right)$ if and only if $\left(\mathfrak{M},M\right)\models \phi \left(\underset{\_}{a}\right)$ for every $a\in M$

Named for logician Leon Henkin (1921–2006), who employed the construction in his proof of the completeness of classical first-order logic.