Zermelo-set-theory


zermelo set theory
mathematics
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.
zermelo fränkel set theory adds the replacement axiom.
[other axioms?]
(1995-03-30)

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