set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any...

of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation (Aussonderung Axiom), subset axiom or axiom schema...

an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage of an axiomatic...

proposed replacing the axiom schema of specification with the axiom schema of replacement. Appending this schema, as well as the axiom of regularity (first...

Axiom of extensionality Axiom of empty set Axiom of pairing Axiom of union Axiom of infinity Axiom schema of replacement Axiom of power set Axiom of regularity...

the standard formulation of the Zermelo–Fraenkel set theory, the axiom of pairing follows from the axiom schema of replacement applied to any given set...

and related operating systems Axiom schema of replacement, a schema of axioms in Zermelo–Fraenkel set theory Replacement rates, in population fertility...

number of cardinalities. Together with the axiom schema of replacement, the axiom of union implies that one can form the union of a family of sets indexed...

existence of the empty set is a theorem. If separation is not postulated as an axiom schema, but derived as a theorem schema from the schema of replacement (as...

range of f, which can be seen to be a set from the axiom schema of replacement. Applying the axiom of regularity to S, let B be an element of S which...