fom
Posts:
1,968
Registered:
12/4/12


Re: Matheology § 223: AC and AMS
Posted:
Mar 15, 2013 7:56 PM


On 3/15/2013 3:01 PM, Virgil wrote: > In article > <c4fcdc6876bb4df0a2f573d117d0b98c@m4g2000vbo.googlegroups.com>, > WM <mueckenh@rz.fhaugsburg.de> wrote: > >> On 14 Mrz., 23:54, fom <fomJ...@nyms.net> wrote: >>> On 3/14/2013 5:47 PM, WM wrote: >>> >>>> On 14 Mrz., 23:16, fom <fomJ...@nyms.net> wrote: >>> >>>>> "... an element of T is not a set..." >>> >>>> Let T = {{a}, {b,c}, {c,d,e,f}} >>>> then T has three elements, each of which is a set. That is common use >>>> in modern set theory and has been used 100 years ago in the same sense >>>> by Zermelo. >>> >>> I am well aware of modern usage. >> >> Zermelo used it already 100 years ago. >>> >>> 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, even if accurate, in no way refutes that Zermelo allowed sets to > contain urelements. In fact, it supports urelements, as otherwise > there would be no reason to specify that those elements all are sets.
It is not accurate. That is where Zermelo is explaining the "general principle of choice". The beginning of the paper in which the domain description is given is on page 201.
For WM's claim (snipped) to be accurate, ZF would have a global choice function.
If it did, I would never have run across the difficulties I had as an undergraduate, and, I would probably have a career in mathematics as a consequence.
So I "know" it to be inaccurate: "proof by reality".
Less subjectively, if it did, no one would speak of models in which the axiom of choice fails.

