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

martdowd at aol.com martdowd at aol.com
Mon May 27 13:48:45 EDT 2013

 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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