Axiomatic set theory is the study of sets in an axiomatic system whose axioms specify which sets
exist and how new sets may be formed. In contrast to naive
set theory , it replaces unrestricted set formation by explicit set-existence
principles.
The principal example is Zermelo-Fraenkel set theory . Adjoining the axiom of choice gives
the commonly used system ZFC. Its restricted formation axioms exclude the construction
underlying Russell's antinomy .
See also Axiom of Choice ,
Axiomatic System ,
Naive Set Theory ,
Russell's
Antinomy ,
Set Theory ,
Zermelo-Fraenkel
Set Theory
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References Curry, H. B. Foundations of Mathematical Logic. Enderton,
H. B. Elements
of Set Theory. Referenced on Wolfram|Alpha Axiomatic Set Theory
Cite this as:
Weisstein, Eric W. "Axiomatic Set Theory."
From MathWorld https://mathworld.wolfram.com/AxiomaticSetTheory.html
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