I'm currently writing my thesis about ZFC origins, and I need a source from where to know who gives the actual first order formulation of ZFC. I got to the point where Bernays writes about it and establishes them, but it seems like a background of NBG. I'm trying also to get access to Skolem's paper of 1929 called Über einige Grundlagenfragen der Mathematik, but I cannot find it anywhere so came here for some help.


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    $\begingroup$ According to the SEP article The Emergence of First-Order Logic, unambiguously first-order formulations of set theory did not appear until the 1930s, by Tarski (1935), Quine (1936), Bernays (1937), and Gödel (1940). See the article bibliography for further details. The article gives details of earlier "near misses" - E.g., Skolem in 1922 "gave the earliest satisfactory first-order formulation of Zermelo’s set theory", but this is heavily qualified. $\endgroup$
    – nwr
    Commented Apr 22, 2021 at 4:15
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    $\begingroup$ You can see van Heijenoort for the "founding fathers": Zermelo, Skolem, von Neumannn. As per comment above, the "first order fragment" of predicate logic was "identified" during the 30s (basically due to Gödel's results). $\endgroup$ Commented Apr 22, 2021 at 6:24
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    $\begingroup$ In the 50s, the standard formulation was available; see e.g Hao Wang, On Zermelo's and Von Neumann's Axioms for Set Theory (1949). $\endgroup$ Commented Apr 22, 2021 at 6:26
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    $\begingroup$ A.A. Fraenkel (the F in ZFC) lists the ZFC axioms in a preface to Bernays' book on NBG, Axiomatic Set Theory. $\endgroup$
    – Spencer
    Commented Apr 27, 2021 at 23:27


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