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)
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