Re: Zuhair's set theory

Zaljohar@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
.

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