FOM: June 1 - June 24, 1999

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FOM: an unusual recursion theory meeting



Dear FOM,

I would like to initiate a discussion of the recent meeting
``Computability Theory and Applications'' (CTA for short),
<http://www.math.psu.edu/simpson/cta/>, June 13-17, Boulder Colorado.

I feel that such a discussion may lead to something of interest
regarding issues and programs in various branches of mathematical
logic, especially recursion theory, and their relationship to f.o.m.

I had high hopes for this CTA meeting.  Before the meeting I wrote (10
Jun 1999 14:12:35):

 > This looks like being an unusual recursion theory meeting.
 > Usually, recursion theorists focus largely on methodological and
 > structural aspects of certain structures (r.e. degrees, etc) that
 > are of interest only to hard-core recursion theorists and have
 > little or no general intellectual interest.  In this meeting, the
 > organizers (Cholak, Lempp, Lerman, Shore) seem to be trying to
 > place more emphasis than usual on what they call ``applications''
 > of recursion theory, i.e. a wider intellectual landscape, including
 > f.o.m.
 > 
 > I applaud this apparent attempt to broaden the scope of recursion
 > theory.  I will report further after the meeting.

My high hopes were not entirely disappointed.  There were a number of
``applied recursion theory'' talks, i.e. talks which tried hard to
connect recursion theory to other subjects.  But I still have to say
that the CTA meeting was a mixed bag in this respect.  In the end, a
preponderance of the talks did focus solely on structural aspects of
r.e. degrees, r.e. sets, etc.  These ``pure recursion theory'' talks
offered little or nothing in the way of f.o.m. motivation, connections
with other subjects, etc.

An interesting feature of the CTA meeting was that all of the speakers
were asked to concentrate on new research directions and open problems
in their respective areas, and many of them attempted to do so.

Below is the program of the CTA meeting, as prepared by Steffen Lempp,
one of the CTA organizers.  A better version of this program,
including abstracts of most of the talks, is available on the web at
<http://www.math.psu.edu/simpson/cta/>.

In future FOM postings, I will comment on some of the talks.  I hope
other CTA participants who are also FOM subscribers (Friedman,
Jockusch, Lempp, Cholak, Hirst, Cooper, ...) will do the same.  Let's
try to get a discussion going.

-- Steve

  Program of the AMS Summer Research Conference on Computability Theory and
     Applications (For general information about this meeting, check the
			    conference home page,
    the AMS summer research conference home page, and the AMS Brochure of
	  Information.) All talks will be held in Engineering 265.
    There will be small classrooms with blackboards available nearby for
			  small-group discussions.

                  Saturday, June 12, 1999                                   
                ARRIVAL 
    5:00-6:00   DINNER                                                       

                  Sunday, June 13, 1999                                        
    Time        Speaker                     Area                             
    6:30-8:00   BREAKFAST                                                  
    8:20-8:25   Steffen Lempp, UW-Madison   Opening Remarks
    8:30-9:15   Sergey Goncharov,           computable model theory 
                Novosibirsk
                BREAK                                
   10:30-10:50  Julia Knight, Notre Dame    models of arithmetic
   11:00-11:20  Serikzhan Badaev, Almaty    numeration theory  
   11:30-1:00   LUNCH                                          
    1:30-2:15   Jeff Remmel, San Diego      computable algebra  
                BREAK
    3:30-3:50   Bakh Khoussainov, Auckland  issues in computable presentations
                                            of models
    4:00-4:20   Mikhail Peretyat'kin        finitely axiomatizable theories
                Almaty                      and Lindenbaum algebras
    5:00-6:00   DINNER              
    evening     WELCOME RECEPTION   

                   Monday, June 14, 1999 
    Time        Speaker                     Area  
    6:30-8:00   BREAKFAST
    8:30-9:15   Peter Cholak, Notre Dame    lattice of computably enumerable 
                                            sets 
                BREAK 
    10:15-11:00 Bob Soare, Chicago          lattice of computably enumerable 
                                            sets 
    11:10-11:30 Klaus Ambos-Spies,          genericity and randomness
                Heidelberg        
    11:30-1:00  LUNCH 
     1:30-4:50  Barry Cooper, Leeds         proof of the automorphism theorem,
                                            part 1 
     5:00-6:00   DINNER
    7:00-10:00  Barry Cooper, Leeds         proof of the automorphism theorem,
                                            part 2  

                  Tuesday, June 15, 1999 
     Time        Speaker                     Area 
     6:30-8:00   BREAKFAST
     8:30-9:15   Andre Nies, Chicago        definability and coding  
                 BREAK 
    10:15-11:00 Richard Shore, Cornell      natural definability in degree 
                                            structures 
    11:10-11:30 Gerald Sacks, Harvard & MIT higher recursion theory
    11:30-1:00  LUNCH 
    afternoon   FREE TIME (for hikes or discussions)
    evening     BARBECUE DINNER (on Flagstaff Mountain)

                 Wednesday, June 16, 1999                        
    Time        Speaker                     Area   
    6:30-8:00   BREAKFAST                                         
    8:30-9:15   Steve Simpson, Penn State   reverse mathematics  
                BREAK                                            
    10:30-11:00 Carl Jockusch, Urbana       Pi01 classes and computable
                                         combinatorics                       
    11:10-11:30 Chi Tat Chong, Singapore    reverse computability theory 
    11:30-1:00  LUNCH           
    1:30-2:15   Harvey Friedman, Ohio State reverse mathematics  
                BREAK                                                        
    3:30-3:50   Sasha Shlapentokh,          issues related to Hilbert's Tenth
                E. Carolina                 Problem 
    4:00-4:20   Anil Nerode, Cornell        computable analysis and topology 
    5:00-6:00   DINNER                                                       

                CONTRIBUTED TALKS           Title                            
    7:00-7:15   Bob Soare, Chicago          Computability and differential    
                                            geometry 
    7:20-7:35   Yuri Ershov, Novosibirsk    Computability in HF over a dense 
                                            linear order
    7:40-7:55   Doug Cenzer, University of  The lattice of Pi01 classes      
                Florida      
    8:00-8:15   Eberhard Herrmann, Humboldt The definability of the          
                University, Berlin          Sigma4-acceptable ideals 
    8:20-8:35   Steve Simpson, Penn State   A Mailing List for Foundations of 
                                            Mathematics  
  
                  Thursday, June 17, 1999                                      
    Time        Speaker                     Area                              
    6:30-8:00   BREAKFAST                                                    
    8:30-9:15   Ted Slaman, Berkeley        applications of recursion theoretic
                                            methods in set theory   
                BREAK   
    10:20-10:50 Alekos Kechris, Cal Tech    Borel equivalence relations       
    11:00-11:20 Marcia Groszek, Dartmouth   independence results (from ZFC) in
                                            recursion theory  
    11:30-1:00  LUNCH                                                        
    1:30-2:15   Manny Lerman, Connecticut   lattice embeddings into the       
                                            computably enumerable degrees
                BREAK                                                         
    3:30-3:50   Andrea Sorbi, Siena         enumeration degrees              
    4:00-4:20   Marat Arslanov, Kazan       d.c.e. and n-c.e. degrees        
    5:00-6:00   DINNER                                                       
   
                   Friday, June 18, 1999                                     
    6:30-8:00   BREAKFAST                                                    
                DEPARTURE                                                    





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