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:
“The writer who neglects punctuation, or mispunctuates, is liable to be misunderstood.... For the want of merely a comma, it often occurs that an axiom appears a paradox, or that a sarcasm is converted into a sermonoid.”
—Edgar Allan Poe (1809–1845)