Definition:Definable/Set

Definition

Let $\MM$ be an $\LL$-structure with universe $M$.

Let $A$ be a subset of $M$.

Let $\LL_A$ be the language formed by adding constant symbols to $\LL$ for each element of $A$.

$A$ is a definable set in $\MM$ if and only if there exists a formula $\map \phi x$ such that:

$a \in A \iff \MM \models \map \phi a$

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 4.15$