Zermelo (1930) is concerned with impredicative second-order set theory. He treats the general case of set theory with urelements, but it will be enough to consider only the case of pure set theory, ie without urelements. In this context, Zermelo's theory is the axiomatic second-order theory T2 in the language of pure set theory whose axioms are Extensionality, Regu [Book Review]

In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 469 (1998)
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Zermelo and set theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
Zermelo: definiteness and the universe of definable sets.Heinz-Dieter Ebbinghaus - 2003 - History and Philosophy of Logic 24 (3):197-219.
In praise of replacement.Akihiro Kanamori - 2012 - Bulletin of Symbolic Logic 18 (1):46-90.
Reply to Crispin Wright and Richard Zach.Ian Rumfitt - 2018 - Philosophical Studies 175 (8):2091-2103.

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