Axiom schema of specification
Concept in axiomatic set theory / From Wikipedia, the free encyclopedia
"Axiom of separation" redirects here. For the separation axioms in topology, see separation axiom.
In many popular versions of axiomatic set theory, the axiom schema of specification,[1] also known as the axiom schema of separation (Aussonderung Axiom),[2] subset axiom[3] or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.
Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension, discussed below.
Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory.[4]