Source : Free On-Line Dictionary of Computing

Zermelo set theory
     
         A {set theory} with the following set of
        {axiom}s:
     
        Extensionality: two sets are equal if and only if they have
        the same elements.
     
        Union: If U is a set, so is the union of all its elements.
     
        Pair-set: If a and b are sets, so is
     
        	{a, b}.
     
        Foundation: Every set contains a set disjoint from itself.
     
        Comprehension (or Restriction): If P is a {formula} with one
        {free variable} and X a set then
     
        	{x: x is in X and P(x)}.
     
        is a set.
     
        Infinity: There exists an {infinite set}.
     
        Power-set: If X is a set, so is its {power set}.
     
        Zermelo set theory avoids {Russell's paradox} by excluding
        sets of elements with arbitrary properties - the Comprehension
        axiom only allows a property to be used to select elements of
        an existing set.
     
        {Zermelo Frankel set theory} adds the Replacement axiom.
     
        [Other axioms?]
     
        (1995-03-30)