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zermelo fränkel set theory

zermelo fränkel set theory in Technology
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.
The Free On-line Dictionary of Computing, © Denis Howe 2010
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