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

[MartDowd at aol.com]

I've been trying to gain some understanding of the notion  of
"inter-universal" in Shinichi Mochizuki's papers.
 
Some useful links:
http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html
Mochizuki's papers.
http://michaelnielsen.org/polymath1/index.php?title=ABC_conjecture
Tons of links
http://en.wikipedia.org/wiki/Abc_conjecture
 
The papers on inter-universality contain copious quantitites of  Diophantine
geometry, but I was hoping to achieve some understanding of the  notion 
anyway.
Some overview papers were little help.  The  paper
INTER-UNIVERSAL TEICHMULLER THEORY I
contains the following  quote:
It is this fundamental aspect of the theory of the present  series of 
papers -
i.e., of relating the distinct set-theoretic  universes associated to the
distinct fiber functors/basepoints on  either side of such a
non-ring/scheme-theoretic filter - that we refer  to as inter-universal.
 
This is still vague.  I suspect the terminology "set-theoretic  universes" 
is
inaccurate, and the author might mean that the data is  heterogeneous, and
should be coded in some (set-theoretic) manner (such as a  tuple).
 
A comment at
http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/#comment-1060
5:
It  seems to me that Mochizuki defines species, mutation and  
morphism-of-mutation
as being whatever defines a category, functor or natural  transformation in 
any
model of ZFC. Thus, by the completeness theorem, these  are nothing but
formalizable-in-ZFC categories, functors, and natural  transformations
 
- Martin Dowd



In a message dated 5/23/2013 2:59:18 P.M. Pacific Daylight Time,  
urquhart at cs.toronto.edu writes:

The  first question is:

"Does the proof contain non-trivial operations  related to changing
the universe in the sense of the foundations of  mathematics or logic?"


-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20130524/9f3b37be/attachment.html>