In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom schema of specification, axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension, is a schema of axioms in Zermelo–Fraenkel set theory. It is also called the axiom schema of comprehension, although that term is also used for unrestricted comprehension, discussed below. Essentially, it says that any definable subclass of a set is a set.
Read more about Axiom Schema Of Specification: Statement, Relation To The Axiom Schema of Replacement, Unrestricted Comprehension, In NBG Class Theory, In Higher-order Settings, In Quine's New Foundations
Famous quotes containing the word axiom:
““You are bothered, I suppose, by the idea that you can’t possibly believe in miracles and mysteries, and therefore can’t make a good wife for Hazard. You might just as well make yourself unhappy by doubting whether you would make a good wife to me because you can’t believe the first axiom in Euclid. There is no science which does not begin by requiring you to believe the incredible.””
—Henry Brooks Adams (1838–1918)