The Free On-line Dictionary of Computing (30 December 2018):

Zermelo Fränkel set theory

    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)