FOM: The work I mentioned in connection to Harvey's

Insall montez at
Wed Jun 19 11:23:57 EDT 2002

The work that I referred to does not explicitly include any demonstrated
equivalences between mathematical statements and large cardinal axioms.  To
some extent, this is because I did not at the time concern myself with large
cardinal axioms.  My co-authors and I realized of course that some fairly
deep foundational considerations play a role in that work of ours, but as I
recall, the term ``large cardinal'' never appears in any of the papers I
cited.  It is the case that in thinking about the ways to prove some of the
results in the papers I cited, I thought about proper classes as being
members of ``larger collections'', always relying foundationally on the idea
that that could be done if enough were assumed in my background set theory.
We have discussed this in this forum before, so I will not delve into the
details.  In separate postings, I shall list some results from those papers,
and comment on variations on the themes developed therein.

Matt Insall
insall at
montez at

Associate Professor of Mathematics
Department of Mathematics and Statistics
University of Missouri - Rolla
Rolla Missouri - USA

Where I ocassionally see a rainbow, or a bluebird, and the smiles on
children's faces are on the backdrop of the rolling Ozark foothills.

More information about the FOM mailing list