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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 223: AC and AMS
Posted: Mar 15, 2013 8:28 PM

In article <wNednaCf1baoKN7MnZ2dnUVZ_hSdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 3/15/2013 3:01 PM, Virgil wrote:
> > In article
> > WM <mueckenh@rz.fh-augsburg.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 ur-elements. In fact, it supports ur-elements, 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.

In other words, WM is quote mining again: isolating quotes from their
contexts in such a way as to misled readers of those quotes or their
original meanings.
>
> 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
> 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.

--

Date Subject Author
3/14/13 Alan Smaill
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 Virgil
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 Virgil
3/19/13 fom
3/19/13 Virgil
3/19/13 Virgil
4/17/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/19/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 fom
4/17/13 Virgil
4/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/16/13 Virgil
3/16/13 Virgil
3/17/13 fom
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/15/13 Virgil
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/15/13 fom
3/15/13 Virgil
3/15/13 fom
3/16/13 Virgil
3/14/13 Virgil
3/14/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom