FOM: The missing 1%

Walter Felscher walter.felscher at
Sun Feb 20 09:15:45 EST 2000

Two historical remarks to this - if I am permitted to say so -
beautifully written article:

> Frege's system of "logic" turned out to be logically inconsistent, as
> discovered by Bertrand Russell, who communicated this to Frege in a letter
> in 1901. (Cantor almost knew about this problem, and used the term
> "inconsistent multiplicities" to refer to the inconsistent objects involved;
> and so did Zermelo). 

As for Zermelo: cf. an article by Ebbinghaus and Thomas in Archiv f"ur
Mathematische Logik und Grundlagenforsch. about 1975 . They quote from
an unpublished letter of Zermelo's .

> Fraenkel added a new axiom, called Replacement and the final axiom system,
> ZFC, was born. (I don't know the exact date for this).

Fraenkel considered such axiom in

  Zu den Grundlagen der Cantor-Zermelo'schen Mengenlehre
  Math.Ann. 86 (1922) 230-237 .

The first precise formulation was given by Thoralf Skolem

  Einige Bemerkungen zur axiomatischen Begr"undung der Mengenlehre.
  Proc. 5th Scand.Math.Congr.Helsinki, 1922 , 217-232 .
  reprinted in: [ed.J.E.Fenstad] Th.Skolem: Selected works in logic. 
  Oslo, 1970, pp.137-152               



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