On 3/15/2013 2:44 PM, WM wrote: > On 15 Mrz., 20:17, fom <fomJ...@nyms.net> wrote: >> On 3/15/2013 3:20 AM, WM wrote: >> >>> On 14 Mrz., 23:54, fom <fomJ...@nyms.net> wrote: >> >>>> Unless my translation is in error, Zermelo's >>>> 1908 supports urelements. >> >>> Zermelo says (in your translation on p. 210, 3rd line): If T is a set >>> whose elements M, N, R, ... all are sets different from the null >>> set, ... >> >> That is Zermelo's description of the >> axiom of choice. > > T is the domain, the set which Zermelo uses to demonstrate his > intention of the axiom of choice.
No. T is an object of the domain Zermelo describes in the beginning of the paper.
> >> It is not the description of his domain. >> >> I gave the relevant passages > > Not for ZFC. There everything is a set.
No. My criticism of Virgil's description of a union was based on the restriction that everything was a set. In standard modern presentations of ZFC unions are defined across the elements because the elements are sets.
In making that criticism, I had to check Zermelo's paper because I had been fully aware that the 1908 in van Heijenoort clearly supported domain objects different from sets.
I verified that memory and noted how it differed from what has become the usual perception because the modern theory generally restricts to pure sets.
Although I generally do not like to restrict discourses to narrow scopes when a general problem domain has not been specified, I certainly do exactly that when one is speaking of what is in print as a historical fact.
One can have errors in translation. One can inadvertently read something into the material. But I have not done that here.