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Zermelo set theory
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mathematics A set theory with the following set of
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
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
is a set.
Infinity: There exists an infinite set.