Definition:Class Intersection/Class of Sets

Definition

Let $A$ be a class.

The intersection of $A$ is:

$\bigcap A := \set {x: \forall y \in A: x \in y}$

That is, the class of all objects which belong to all the elements of $A$.

Also see

• Intersection of Class Exists and is Unique
• Intersection of Non-Empty Class is Set
• Intersection of Doubleton

• Results about class intersection can be found here.

Sources

• 2002: Thomas Jech: Set Theory (3rd ed.) ... (previous) ... (next): Chapter $1$: Separation Schema
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 5$ The union axiom