# [FOM] Disguised Set Theory "DST"

Frode Bjørdal frode.bjordal at ifikk.uio.no
Thu Oct 6 17:54:52 EDT 2011

```So I plead guilty to having counted wrongly in my previous post where
I clarified that and how the presentation of DST had created
confusion, and not only with me. I should have stated that I had
three, not two, previous posts on this matter. I predict that there in
all will be five and hope my prophetic abilities are better than the
ones I made apparent for track keeping.

Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslo
www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html

2011/10/6 Zuhair Abdul Ghafoor Al-Johar <zaljohar at yahoo.com>:
> Dear F.Bjordal
>
> No you are using the original definition of x', which cannot be
> used in disguised formulas. The definition that can be used
> is that one you presented about z'Ey and this one unlike the
> original definition can allow some sets that have the same
> E-members of z' to be E-elements of y.
> So a set x such that x={x,0} has the same E-elements
> as the set {0}, they don't have the same e-elements
> as you are alluding to in your argument. The problem
> is that we may have a hierarchy of 0, x={x,0}, x1={0,x,x1}
> ,x2={0,x,x1,x2},...... where xi=xj iff i=j. Accordingly
> only 0 is shared between all inductive sets so N={0}.
> The sole problem is that we don't have a proof of exclusion
> of parallel routs to that of finite V.N ordinals, so we
> cannot exclude the case where N={0}.
>
> Regards
>
> Zuhair
>
>
>
> At Tue, 4 Oct 2011 17:55:16 +0200; Frode Bjordal wrote:
>
>
>> It does not seem to me that what I wrote up has been
>> rendered in a
>> faithful faithful manner here.  I defined
>> z'={u:uEzVu=z}. How would
>> one arrive at a fixed point x={?,x} with x=?'? Then we
>> would have
>> {u:uE?Vu=?}={x:x=?Vx={u:uE?Vu=?}. That cannot be reasonable.
>> Ordinal
>> succession as I defined it was anchored in ? and succeeds
>> along the
>> von Neumann ordinals.
>>
>>
>>
>> --
>> Frode Bj?rdal
>> Professor i filosofi
>> IFIKK, Universitetet i Oslo
>> www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
>>
>>
>> ------------------------------
>>
>
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