[1] : The Free On-line Dictionary of Computing (27 SEP 03)

zermelo set theory
     
         a set theory with the following set of
        axioms:
     
        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 px.
     
        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
     
     
see also:
set theory axiom a, b formula free variable x: x is in x and px 
infinite set power set russell's paradox zermelo frankel set theory 

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