The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel
set theory is replaced by
6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula 
, 
,
which can be deduced from Axiom 6. However, there seems to be some disagreement in the literature about just which axioms of Zermelo-Fraenkel
set theory constitute "Zermelo Set Theory." Mendelson (1997) does not
include the axioms of choice, foundation,
replacement In Zermelo set theory, but does
includes 6'. However, Enderton (1977) includes the axioms
of choice and foundation, but does not
include the axioms of replacement or Selection.
See also
Set Theory,
Zermelo-Fraenkel
Set Theory
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References
Enderton, H. B. Elements of Set Theory. New York: Academic Press, 1977.Mendelson, E.
Introduction
to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.Iyanaga,
S. and Kawada, Y. (Eds.). "Zermelo-Fraenkel Set Theory." §35B in Encyclopedic
Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 135, 1980.Zermelo,
E. "Über Grenzzahlen und Mengenbereiche." Fund. Math. 16,
29-47, 1930.Referenced on Wolfram|Alpha
Zermelo Set Theory
Cite this as:
Weisstein, Eric W. "Zermelo Set Theory."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZermeloSetTheory.html
Subject classifications
