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

[Kevin Watkins]

According to Wikipedia
(http://en.wikipedia.org/wiki/Shinichi_Mochizuki), Japanese
mathematician Shinichi Mochizuki has written a series of papers that
claim to prove the abc conjecture in number theory.

The fourth of these papers contains a section which the abstract of
the paper describes as treating set-theoretical/foundational issues.

I thought this list's readers might be in a position to comment on its
significance.

Kevin

>From the abstract:

Finally, we examine — albeit from an extremely naive/non-expert point
of view! — the foundational/settheoretic issues surrounding the
vertical and horizontal arrows of the log-theta-lattice by introducing
and studying the basic properties of the notion of a “species”, which
may be thought of as a sort of formalization, via set-theoretic
formulas, of the intuitive notion of a “type of mathematical object”.
These foundational issues are closely related to the central role
played in the present series of papers by various results from
absolute anabelian geometry, as well as to the idea of gluing together
distinct models of conventional scheme theory, i.e., in a fashion that
lies outside the framework of conventional scheme theory. Moreover, it
is precisely these foundational issues surrounding the vertical and
horizontal arrows of the log-theta-lattice that led naturally to the
introduction of the term “inter-universal”.

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf