Free On-line Dictionary of Computing:
zermelo fr
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)
