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 P. 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 Fränkel SET theory adds the Replacement axiom. [Other axioms?] (1995-03-30)
