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🏠
/
Mathematics
/
Set Theory
/
Axiom schema of specification (or of separation, or of restricted comprehension)
Axiom schema of specification (or of separation, or of restricted comprehension)
Allows the construction of a subset of a set
A
A
A
defined by a logical formula
ϕ
\phi
ϕ
.
📜
The statement of the theorem
∀
z
∃
y
∀
x
(
x
∈
y
⟺
x
∈
z
∧
ϕ
(
x
)
)
\forall z \exists y \forall x (x \in y \iff x \in z \land \phi(x))
∀
z
∃
y
∀
x
(
x
∈
y
⟺
x
∈
z
∧
ϕ
(
x
))
.