Word for objects satisfying a formula

Question

Is there a word in logic for the class of individuals satisfying a given formula $\varphi$ ? I am also looking for a word for the individual obtained by interpreting the singular term $\iota v \varphi$ (provided it exists)?

Answer 1

For : $\iota v \varphi(v)$ see Definite description :

it means "the unique object $v$ such that $\varphi(v)$".

For the class defined by the property $\varphi(x)$, i.e. $\{ x \mid \varphi(x) \}$, sometimes I've read truth-set.

In traditional logic the extension of a concept consists of the things to which it applies.