Q:\CHOICE\RUBIN.TXT            2001 May 9

references:

Herman Rubin and Jean E. Rubin, "Equivalents of the Axiom of Choice,"
North-Holland Publishing Company, Amsterdam, 1963.

Jean E. Rubin, "Set Theory for the Mathematician," Holden-Day Inc.,
San Francisco, 1967.

According to Rubin and Rubin (1963), the following formulation of the
axiom of choice was stated in 1906 by Bertrand Russell, and in 1908
by Zermelo:

  If  t  is a disjoint collection of nonempty sets, there exists a set
  C  which consists of one and only one element from each set in t.

The references given are:

Bertrand Russell, 1906, "On some difficulties in the theory of 
transfinite numbers and order types," Proc. London Math. Soc. (2) 
vol. 4, pp. 29-53.

E. Zermelo, 1908, "New proof for the wellordering," Math. Annalen
vol. 65, pp. 107-128. [in German]

There is also an earlier 1904 paper by Zermelo on the well ordering 
theorem:

E. Zermelo, 1904, "Proof that every set can be wellordered," Math.
Annalen vol. 59, pp. 514-516.

English translations for both of Zermelo's papers are given in
van Heijenoort's source book (1967).

Jean van Heijenoort, 1967, "From Frege to G\"odel.  A Source Book
in Mathematical Logic, 1879-1931," Harvard University Press,
Cambridge, Massachusetts.