Full Idea
Zermelo proposed seven axioms for set theory, with Fraenkel adding others, to produce the standard Z-F Intuition.
Gist of Idea
The standard Z-F Intuition version of set theory has about ten agreed axioms
Source
report of José A. Benardete (Metaphysics: the logical approach [1989], Ch.17) by PG - Db (ideas)
Book Reference
Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.124