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I have googled the heck out of this but cannot find a reference to the year Z&F published their axioms. I'd expected to see an article reference but none that I could find.

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  • $\begingroup$ The ZF axioms weren't really adopted as the default standard until the second half of the 20th century. You had Kelley's 1955 textbook on general topology having to give an appendix with set theory axioms, and they are a variant now known as Morse-Kelley set theory, and it isn't equivalent to ZFC in strength. The history of set theory axioms is surprisingly twisty and not always named after the actual people. See also en.m.wikipedia.org/wiki/… $\endgroup$ Commented Feb 6, 2022 at 7:43
  • $\begingroup$ As a result, people were at such a distance from the original sources when they became "standard", most mathematics in practice is insensitive to foundations, and in fact most mathematicians can't even quote the actual ZFC axioms, that people never think to have a source to quote. $\endgroup$ Commented Feb 6, 2022 at 7:45

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See The development of Set Theory and Zermelo’s Axiomatization of Set Theory:

  • Ernst Zermelo, 1908 paper “Untersuchungen über die Grundlagen der Mengenlehre, I” (1908) and “Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre” (1930);

  • Abraham Fraenkel, "Über den Begriff "definit" und die Unabhängigkeit des Auswahlaxioms," (1922) and "Untersuchungen über die Grundlagen der Mengenlehre" (1925).

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    $\begingroup$ E. Zermelo, "Untersuchungen über die Grundlagen der Mengenlehre. I," Mathematische Annalen, Vol. 65, No. 2, June 1908, pp. 261-281 (online). Adolf Fraenkel, "Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre," Mathematische Annalen, Vol. 86, No. 3, September 1922, pp. 230-237 (online). The latter contains the Ersetzungsaxiom (axiom of replacement). $\endgroup$
    – njuffa
    Commented Jan 28, 2022 at 19:36
  • $\begingroup$ See also en.wikipedia.org/wiki/… $\endgroup$ Commented Feb 6, 2022 at 7:46

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