FOM: FOM faces at ASL 2000; themes of the meeting

[Stephen G Simpson]

Harvey Friedman writes:

 > The year 2000 meeting of the ASL held in Urbana, June 3 - 7, 2000,
 > was exciting, enjoyable, and thought provoking.

Yes, yes, yes.  

I particularly enjoyed meeting a lot of FOM personalities
face-to-face, in some cases for the first time.  Among the FOM faces
at ASL 2000 were: Avigad, Awodey, Bauer, Buss, Butz, Cherlin, Cholak,
Cook, Davis, Dawson, Feferman, Ferreira, Frank, Friedman, Gao, Hirst,
Jockusch, Kechris, Khoussainov, Knight, Lempp, Lerman, L"owe, MacLane,
Maddy, Marcone, Marker, Martin, Parsons, Pillay, Rathjen, Ross,
Ruitenburg, Scott, Shoenfield, Sieg, Simpson, Soare, Steel, Stout,
Tait, Trimble, Urquhart, van den Dries, Wood.

It was great to see all of you, and I appreciated all the FOM
follow-up and feedback.  It is clear that FOM is having a substantial
impact in the logic community.

 > There a number a thoughts I had during the meeting, only a fraction
 > of which came to the surface.

Me too.  I will post some of my thoughts when I get time.  For now let
me try to indicate some broad themes.

Although there was some discussion of f.o.m. issues at the meeting,
there was not as much f.o.m. as I would have liked.  The division of
logic into specialized subfields (set theory, model theory, recursion
theory, proof theory, etc) was very much in evidence, and it seems
that this regrettable (from my point of view) trend is continuing and
perhaps even accelerating.

On the other hand, the organizers of ASL 2000 obviously went out of
their way to encourage discussion of broad trends in logic.  In
addition to the New Axioms panel which has been aired rather
thoroughly here on FOM, there were other panels on the history of
logic in the 20th century, and the future of logic in the 21st
century.  It is true that the panelists omitted some very significant
trends in logic and f.o.m.  Yet, many of the panelists and other
speakers did attempt to take a broad view of at least their own
subfields of logic, and that was all to the good.

A persistent undercurrent of ASL 2000 was a concern with applications
and connections of logic to other fields, anxiety over the need to
``sell'' or ``peddle'' logic to outsiders, etc.  This theme surfaced
in various ways:

1. the set theorists' emphasis on descriptive set theory and
   its connections to core math;

2. the applied model theorists' emphasis on applications and
   connections of model theory to core math, via o-minimality and
   ``geometric model theory'';
 
3. Soare's emphasis on applications of recursively enumerable sets to
   Riemannian geometry via ``basins'';

4. the proof theorists' emphasis on connections between proof theory
   and computer science, including complexity, automated reasoning,
   etc.;

5. last but not least, Harvey's vigorous attempt to convince set
   theorists, logicians, and core mathematicians of the value of
   Boolean relation theory.

I plan to comment more later on these and other themes that emerged at
the ASL 2000 meeting.  I hope others will do the same.

-- Steve