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Topic: Matheology § 288
Replies: 160   Last Post: Jun 21, 2013 8:42 AM

 Messages: [ Previous | Next ]
 Ralf Bader Posts: 488 Registered: 7/4/05
Re: Matheology § 288
Posted: Jun 20, 2013 11:42 PM

Julio Di Egidio wrote:

> "FredJeffries" <fredjeffries@gmail.com> wrote in message

>> On Jun 20, 10:46 am, "Julio Di Egidio" <ju...@diegidio.name> wrote:
>>> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

>>> > On 20 Jun., 15:33, "Julio Di Egidio" <ju...@diegidio.name> wrote:
>>> >>
>>> >> (E.g. did anybody study the latter construction [the L=[0,L]]? Does
>>> >> the "issue" exists at all,

>>>
>>> > This issue does not exist in any forum or journal where matheologians
>>> > are the dominating fraction.

>>>
>>> If that distinction has any merit, then it's hard to believe that nobody
>>> has
>>> looked into it yet. Anyway, if that is so, this "issue" might very well
>>> become the basis for my PhD thesis... so to speak.

>>
>> it seems that you wish to abolish limit ordinals and relabel the
>> successor of a limit ordinal to the limit ordinal's label, etc. Thus,
>> is currently called omega + 1, your omega + 1 is what is now referred to
>> as omega + 1, omega + omega for you would be (omega + omega + 1)...
>>
>> Is that close?
>>
>> Is there some problem you believe you can solve with such a system?

>
> These are the two core posts:
>
>
> The idea was not just that of a shift of labels:
>
> Consider von Neumann definition of ordinals: "each ordinal is the
> well-ordered set of all smaller ordinals. In symbols, lambda = [0,
> lambda)."
>

<http://en.wikipedia.org/wiki/Ordinal_number#Von_Neumann_definition_of_ordinals>
>
> Now consider this alternative definition: each ordinal is the well-ordered
> set of all non-strictly smaller ordinals. In symbols, lambda = [0,
> ambda]. -- I.e. the set includes the ordinal to which it corresponds.
>
> That's what I am asking about, the second definition: if it works, if it
> exists in the literature, etc.
>
> By the way, thanks very much for the references you give in the other
> post.
>
> Julio

By foundation, no set in ZFC can contain itself as an element. Moreover, in
the development of ZFC, an ordinal is by definition a hereditarily
transitive set. A set S is transitive if any one of its members is also a
subset; that is, x e X c S entails x e S. And "hereditarily" means that all
elements of S share the property referred to, so here are themselves
transitive. The von Neumann ordinals are the ordinals according to that
definition. A von Neumann ordinal is well-ordered by the e-relation, i.e., x
is less than y in that order if x is an element of y. And then one proves
that any well-ordered set is order-isomorphic to an ordinal. Then comes
transfinite induction, cardinals are by definition ordinals of a special
kind, and so on. This is basic stuff in any textbook or lecture on set
theory. Take any one and see what happens with your proposal - I'd say it
will be a trainwreck.

Date Subject Author
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 apoorv
6/17/13 Virgil
6/17/13 apoorv
6/17/13 Virgil
6/17/13 Tanu R.
6/17/13 Virgil
6/17/13 fom
6/16/13 FredJeffries@gmail.com
6/16/13 apoorv
6/16/13 apoorv
6/17/13 FredJeffries@gmail.com
6/17/13 Virgil
6/17/13 FredJeffries@gmail.com
6/18/13 LudovicoVan
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Virgil
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/19/13 Virgil
6/19/13 Virgil
6/18/13 Virgil
6/18/13 fom
6/18/13 fom
6/18/13 LudovicoVan
6/18/13 fom
6/19/13 LudovicoVan
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 LudovicoVan
6/19/13 fom
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 Virgil
6/20/13 Virgil
6/20/13 FredJeffries@gmail.com
6/20/13 LudovicoVan
6/21/13 LudovicoVan
6/21/13 LudovicoVan
6/20/13 FredJeffries@gmail.com
6/20/13 Virgil
6/20/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/17/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/15/13 Tanu R.