Database: Axiom of Difference

Axiom 68: Difference

For all classes \mathcal{X} and \mathcal{Y} there exists a class \mathcal{D} such that for each set z we have z \in \mathcal{D} if and only if z \in \mathcal{X} and z \notin \mathcal{Y} .

This database entry builds on the following:

  1. Terminology: Class, membership
  2. Terminology: Axiom
  3. Definition: Conjunction
  4. Definition: Existential quantification
  5. Definition: Equivalence
  6. Definition: Set, proper class
  7. Definition: Universal quantification
  8. Definition: Bounded universal statement
  9. Definition: Negation of binary predicates