Axiom:Axiom of Specification/Also known as

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The Axiom of Specification is also known as:

  • The Axiom of Subsets (although this unnecessarily reduces the scope of this axiom to pure set theory)
  • The Axiom of Comprehension
  • The Axiom of Selection (this axiom allows one to select the elements of a subset)
  • The Axiom of Separation or Separation Principle (although this can be confused with the Tychonoff separation axioms, which arise in topology, so this name is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$)
  • The Axiom of Segregation, under its German name Aussonderungsaxiom
  • The limited abstraction principle, in apposition to the unlimited abstraction principle, also known as the comprehension principle.
  • In the context of class theory, the term Axiom of Class Formation is often seen.