## 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.

Last updated: 1995-04-10

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**Nearby terms:**
zen « ZENO « zepto « **Zermelo Fränkel set theory** » Zermelo set theory » ZERO » zero

Copyright Denis Howe 1985