zermelo frankel set theory

1 definition found

zermelo frankel set theory - Free On-line Dictionary of Computing (26 May 2007) :

  Zermelo Frankel 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)