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From The Free On-line Dictionary of Computing (27 SEP 03) : [ foldoc ]
Zermelo Frankel set theory
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)