[FOM] My claim that ZF proves: "There are no weakly inaccessible cardinals."

Marc Alcobé malcobe at gmail.com
Sat Aug 20 12:07:26 EDT 2011

I have not tried to read the material at length yet, but I would ask
the author to offer, if possible, a bird's eye outline of the proof
trying to leave aside his concerns about the technical details and any
reference to his previous work. Say, one that could be understood by
someone who has read just Jech's Set Theory. That would really help to
start evaluating it.

The author certainly seems to try so when he claims something like (p. 16):

"The required contradiction can be attained by means of creation some
matrix function which should possess inconsistent properties:
it should be monotone and at the same time it should be deprived its

But this does not do the job, since it is not clear what is meant by
matrix functions or their monotonicity. Actually, what I retain from
such a claim is:

"The required contradiction can be attained by creating a function
with inconsistent properties."

And I think this still cast doubts about what the author means by
"creating a function", like the first of those expressed by Michael

The only reasonable interpretation I can think of for that claim is
that the author can exhibit, or prove that he could in principle
exhibit, two formulas: one that defines the class of the elements of
the domain of the function, and another one that defines the function
over that domain, such that there are three proofs: one that the
domain of the function is not empty, another one that shows one
property of that function over that domain, and another one that shows
the negation of that property for that function over the same domain.

This looks a lot more like a plan for a proof to me, but, of course, I
do not know if this is remotely similar to the plan the author has
followed. I have only tried to give an example of what I think it
could be a comprehensible outline of the proof to me, given the
author's claim.

2011/8/19 Alexander Kiselev <aakiselev at yahoo.com>:
> 1) The statement that this claim is regarded as very dubious is not
> based on anything.
> 2) Links in the posted FOM message are  not proper  and the correct link is
> <http://lanl.arxiv.org/find/all/1/ti:+AND+Inaccessibility+Subinaccessibility/0/1/0/all/0/1>
> Sincerely   yours,                              Alexander  Kiselev
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