Zermelo Fränkel set theory

<mathematics>

A set theory with the axioms of Zermelo set theory (Extensionality, Union, Pair-set, Foundation, Restriction, Infinity, Power-set) plus the Replacement axiom schema:

If F(x,y) is a formula such that for any x, there is a unique y making F true, and X is a set, then 

 {F x : x in X}
is a set. In other words, if you do something to each element of a set, the result is a set.

An important but controversial axiom which is NOT part of ZF theory is the Axiom of Choice.

Last updated: 1995-04-10

Nearby terms:

ZENO ♦ zepto ♦ Zermelo Fränkel set theory ♦ Zermelo set theory ♦ ZERO

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