Free On-line Dictionary of Computing:
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 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.
