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Axiom schema of specification
In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme 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 Godel considered it the most important axiom of set theory.[1]
Contents
1 Statement
2 Relation to the axiom schema of replacement
3 Unrestricted comprehension
4 In NBG class theory
5 In higher-order settings
6 In Quine's New Foundations
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