Source : Free On-Line Dictionary of Computing

Zermelo Frankel set theory
     
         A {set theory} with the {axiom}s 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)