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*To*: fom@math.psu.edu*Subject*: FOM: an unusual recursion theory meeting*From*: Stephen G Simpson <simpson@math.psu.edu>*Date*: Mon, 21 Jun 1999 14:53:41 -0400 (EDT)*Organization*: Department of Mathematics, Pennsylvania State University*Reply-To*: simpson@math.psu.edu*Sender*: owner-fom@math.psu.edu

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

**Follow-Ups**:**Stephen G Simpson**- FOM: an unusual recursion theory meeting; impressions of CTA talks

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