Definition:Class Intersection/Class of Sets
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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