Re: Inaccessible cardinal.

On Nov 26, 4:11 pm, Zaljo...@xxxxxxxxx wrote:
On Nov 25, 2:22 pm, Zaljo...@xxxxxxxxx wrote:





Hi all,

In a previous thread in this usenet- topic: V , Rupert has defined
inaccessible cardinal in the following manner:

x is inaccessible cardinal <->

Ay(y subnumerous to x->(Az((there exists a surjection from P(y) to z)->z is subnumerous to x))) & (Ay(y subnumerous to x & Az(z e y -> z

subnumerous to x)) -> Az(there is a surjection from the union of y to
z -> z is subnumerous to x)) .

The paranthesis are somewhat confusing in this definition:

Perhpas Rupert meant the following:

x is inaccessible cardinal <->

[ Ayz((y subnumerous to x & there is a surjection from P(y) to z)
->z is subnumerous to x)
&
Ayz((y subnumerous to x & Am(m e y -> m subnumerous to x) & there is
a surjection from the union of y to z) ->
z is subnumerous to x) ].

Is that correct?

Zuhair

Suppose we have a theory T such that a class V of all sets is provable
to exist in this theory.

Now suppose that ANY k-inaccessible cardinal (proved to exist by ZF+ k
inaccessible cardinals exist) would be provable to exist in V in
theory T.

Now what would be the size of V.

Zuhair- Hide quoted text -

- Show quoted text -

R =A(y),A(x) //bijection assumed.
E = A(ey)<->A(ex) // but not cardinally paired within in or_not_time=
m.
E' =A(ex')|A(ey') //where lor x, lor y=Z(a',b',c'...)

|| RE' |%^a|| //bridge function is order bijection if and only if
Z(ey',ex')<->AyAx can satisfy the transform R^2*(R/l)|->S*(m/l) where
S = 0.p.+(ea'-n) where ea'-n=1

where l = length Time = 0 following the premise that Time length is an
impossible quatity to measure.

Still, one can class it in terms subnumeral, but I'm stopping there.
The form given has no contradictions, and the bridge function and
transform will satisfy the Hunia's Trinity law, and the conditional
law of inversion for bijection, injection and surjection where pairing
elements to cardinality equivalence.

Please Site as Spade bridge function.
.