replacement, axiom of

replacement, axiom of
The axiom added to Zermelo's set theory by A. A. Fraenkel (1891–1965), to produce the classical set theory known as ZF. Put in terms of second-order logic, the axiom states that any function whose domain is a set has a range which is also a set. That is, if the arguments of a function form a set, so do the values of the function. This formulation is second-order because it quantifies over functions; in first-order logic the axiom needs to be stated as an axiom schema. See also Zermelo–Fraenkel set theory.

Philosophy dictionary. . 2011.

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