from
The Free On-line Dictionary of Computing (8 July 2008)
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}.
(1995-04-10)