Re: Simplifying M theories.
- From: zuhair <zaljohar@xxxxxxxxx>
- Date: Mon, 22 Jun 2009 17:58:54 -0700 (PDT)
On Jun 22, 5:48 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Jun 22, 3:21 pm, zuhair <zaljo...@xxxxxxxxx> wrote:
Just point out the mistakes.
Better would be for you to start by giving the exact formulas you
purport to prove rather than handwaving descriptions such as "when we
apply them to sets".
It can be done. a simple sketch would be
0 is a universe, Power 0 would be a universe
acutally it can be proved that for any unvierse , then its power is a
universe.
and that every universe is a set.
Now take the class of all finite ordinals, (it can be proved that
every finite ordinal is a set), now from comprehension you'll have the
"class" of all finite ordinals which is unique, and this is Omega.
Now the class of all unvierses is also provable to exist from
comprehension and proved to be unique from extensionality.
it is easy to prove that the class of all universes is infinite.
lets take a subset of this class which is the class of all universes
were there exist a finite ordinal that is a subset of them but not a
member of them, and where every subset x of them that is a universe
there exist a member in them such that the power set of it is that
subset x.
These will be the powers of 0.
it is not diffuclt to see that this class is equinumerous to omega
(ordered pairs between these two classes can be proved to be sets,
thus the cartesian products of the class of these powers, and Omega is
provable from comprehension, and subsets of it (relations) are
provable from comprehension. thus equinumerousity between the class of
powers of empty set and Omega can be proved, and thus this class would
be countable thus the union of it would be a universe.
The proof is long, and I don't want to go to its details. since I
already reached to a better theory than that.
Zuhair
Also, before listing an axiom that uses defined function or predicate
symbols, please provide those definitions, and even before that,
provide proofs of whatever existence/uniqueness theorem supports the
definition.
I'll do that when my ideas about theories M finalize. I will give the
details
MoeBlee
.
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