[FOM] Shinichi Mochizuki on set-theoretical/foundational issues

[Robert Solovay]

Can you explain "fibres of V \times V"?

-- Bob Solovay
On May 27, 2013 12:39 PM, <martdowd at aol.com> wrote:

>
>  Following are some comments on recent posts on this
> thread:
>
> 1.  Yoneda's lemma, as stated in
>  Categories for the Working Mathematician
> by Saunders MacLana,e can be formalized in NBG.  The naturality claims can
> be
> "unwound", and considering Set^D is avoidable.  Alternatively, Set^D can be
> considered a definable type 2 object.
>
> 2.  Mochizuki's use of the term "set-theoretic universe" seems to require a
> system of "parallel" universes.  Grothendieck universes form a chain under
> inclusion.  Even if there were any advantage to "parallel universes", they
> could be formalized as fibers of V \times V.
>
> - Martin Dowd
>
> It is clear he sometimes uses the term "universe" this way.
>
>
>
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