Re: Multilayer Set Theory:

On May 27, 10:31 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
On 2007-05-27, in sci.math, zuhair wrote:

Have you come across such theories like the ones I have presented in
this thread before?

As said, it's just omega-order ZFC. That is, if you got the details right; I
didn't go through your presentation in detail. Its natural models are of the
form V_kappa+omega for an inaccessible kappa. There's not much more to say
unless you explain specifically what you're looking for.


Aatu says : 'it's just Omega-order ZFC'.

you are saying it as if it is nothing.
It is a one sorted FOL theory that is equi-interpretable with Omega
order-ZFC; to you that is nothing.
Omega order theories are complex theories in comparison to
one sorted FOL theory. So if one has
a one sorted FOL theory that is equi-interpretable with
and Omega order theory then that should be something.
I would personally choose the simpler theory, since
it is more convinient to work with a simpler theory.

This theory reduces a theory that is writtin in
Omega sorted first order logic (Auto
calls it Omega order theory )
to a theory writtin in ONE sorted first order logic.
And it is nothing???

For instance what theory would be equi-interpretable
with Omega order oo-Multilayer? would it be w^2 order ZFC?
do such a theory exist?

Zuhair

.