Re: Zuhair's set theory
- From: Zaljohar@xxxxxxxxx
- Date: Sat, 27 Oct 2007 15:21:37 -0700
On Oct 27, 8:42 am, Jan Burse <janbu...@xxxxxxxxxxx> wrote:
Zaljo...@xxxxxxxxx schrieb:
> y=Tc(x) <-> ( Am(mex->mey) & y is transitive &
> Am( (mey & ~mex) -> Ez( zey & mez ) ) ).
Because you have an according axiom this
is well defined. But is the axiom consistent?
First lets challenge uniqueness:
Take x={0}
And y1={0,0',0'',0''',0''',..}
And y2={0,0',0'',0''',0''',..,y1,y1',y1'',..}
Where 0={},
and n'=n u {n}.
We have:
x subset y1, y1 transitive, y1\x has successors
x subset y2, y2 transitive, y2\x has successors
I think your 2) Axiom of Transitive closure is
not a good idea. It would prevent some simple
sets such like omega+omega from (y2) existence.
Bye
omega+omega do exist in this theory.
it is a theorem of this theory that Tc(w+w) = w+w
I don't see any problem of uniqueness,
Zuhair
.
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