FOM: beauty test

[Harvey Friedman]

Evidence is coming in from my contacts in the mathematics community outside
the logic community.

The evidence indicates that the independent statement (Proposition 1) and
the classification (Theorem 4) in posting

#125:Disjoint Unions/First Classifications, 6:19AM  3/1/02

is getting a new level of reaction. The reaction is characterized by the term

*beautiful*.

This is not a well defined scientific term. However, it is a highly
positive assessment from professional mathematicians, and is about the most
that can generally be expected when they are assessing work outside their
immediate areas of expertise.

For example, in their own area of expertise they sometimes use words like
"breakthrough", "tour de force", "defining moment", "revolutionary",
etcetera.

"Beautiful" is very strong, and it is much stronger than, say, "natural".

A consensus opinion of "beautiful" is sufficient to be confident that the
work - particularly of this very elementary character - will be taken up
and developed by significant mathematicians.

We can now be fully confident that Boolean relation theory is going to
realize its expectations, and thereby position modern set theory and large
cardinals properly in the future development of mathematics.

HOW DO WE KNOW THAT MY RESULTS ARE CORRECT? THIS IS ESSENTIAL FOR SUCH
DISCUSSION. I PLAN TO HAVE A FINISHED MANUSCRIPT SUBMITTED FOR PUBLICATION
WITHIN 6 WEEKS, AND AVAILABLE ON THE WEB.