FOM: Lempp/Friedman correspondence; where are the recursion theorists?

[Stephen G Simpson]

Dear FOM subscribers,

Here is some more off-line discussion of issues and programs in
recursion theory.  (Note: This material has been slightly edited.)

So far, the participants in this discussion are myself, Steffen Lempp,
and Harvey Friedman.  I would like to draw in more participants.
Where are all the recursion theorists?  In particular, where are Bob
Soare, Richard Shore and Ted Slaman?

-- Steve

  -----

  From: Steffen Lempp <lempp at math.wisc.edu>
  To: friedman at math.ohio-state.edu, simpson at math.psu.edu
  Subject: your comments on FOM
  Date: Mon, 10 Aug 1998 10:26:59 +0100 (MET)
  
  Dear Harvey and Steve,
  
  Thanks to both of you for your thoughtful comments, and to Steve for
  forwarding them to me here in Siena.
  
  I believe that logic in general, and recursion theory in particular,
  is already undergoing some profound changes.
  
  Let me start with the example of the Turing degrees globally, and
  the r.e.  Turing degrees, dear to me, and to me simply two beautiful
  mathematical structures: A number of problems about this structure
  were posed in the 1960's (algebraic structure, definability
  questions, homogeneity, rigidity) which turned out to be very hard
  to answer and which took a lot of technical work. The early 1990's
  have seen some spectacular developments, and most of these problems
  have now been solved, using all the very technical and hard results
  that turned off a lot of people in the meantime. This is regrettable
  but, given the difficulty of the structure, unavoidable.
  
  But recursion theory is not only degree theory. There has always
  been a lot of work in Russia, and more and more in the U.S., on
  applications to algebra and model theory. Some of the work has not
  been very enlightening (but of the kind you mention), but a lot of
  it has been very interesting, and the field still seems in its
  infancy.
  
  Another application of recursion theory has been seen in recent work
  by Slaman et al. in descriptive set theory, using recursion
  theoretic methods to solve long-standing problems there.
  
  You mention reverse mathematics. Remember that many results there
  are using techniques developed by classical recursion theorists
  working on "uninspiring topics". This simply shows me that
  intrinsically interesting, beautiful mathematics will survive and
  find applications no matter what. I welcome the strong connections
  between recursion theory and reverse mathematics that emerge, and I
  agree that there are a number of interesting problems in reverse
  mathematics (some quite deep, some more ad hoc).
  
  What I do object to is people trying to decide what is (objectively)
  interesting mathematics and what isn't. This will always be
  subjective, in the judgment of each researcher, and there will
  always be disagreements. I do believe that while we certainly hav
  every right to voice our views, we should be tolerant and respectful
  of each other's mathematical tastes.
  
  Best regards,                           Steffen
  
  -----
  
  From: Harvey Friedman <friedman at math.ohio-state.edu>
  To: Steffen Lempp <lempp at math.wisc.edu>
  Cc: simpson at math.psu.edu
  Subject: Re: your comments on FOM
  Date: Mon, 10 Aug 1998 21:48:02 +0100
  
  Dear Steffen,
  
  I have much to say about your interesting letter, especially the
  last paragraph. But I was looking forward to this being conducted
  openly on the FOM. I think it would simplify matters if you would
  become a subscriber and post your views directly on the FOM.
  
  I think it makes much more sense to have an open dialog about these
  issues - even metaissues such as what issues we should have an open
  dialog about.  There are over 300 people on this list, including
  some recursion theorists.  The issues and metaissues are definitely
  going to be openly discussed there in a candid way, anyways.
  
  >What I do object to is people trying to decide what is
  >(objectively) interesting mathematics and what isn't. This will
  >always be subjective, in the judgment of each researcher, and there
  >will always be disagreements. I do believe that while we certainly
  >hav every right to voice our views, we should be tolerant and
  >respectful of each other's mathematical tastes.

  Let me just say, briefly, that in my opinion, there are important
  objective components to this, and that the collective judgments
  determine the levels and nature and effectiveness of employment,
  recognition, influence, education, and communication - in fact, even
  the very survivability of subjects. From your persepctive, perhaps
  Steve and I are intolerant. From my perspective, many subcommunities
  and individuals are intolerant, and we are interested in reform. I
  have more to say about this.

  Harvey

  -----
  
  From: Steffen Lempp <lempp at math.wisc.edu>
  To: Harvey Friedman <friedman at math.ohio-state.edu>
  cc: simpson at math.psu.edu
  Subject: Re: your comments on FOM
  Date: Tue, 11 Aug 1998 02:20:00 -0500 (CDT)
  
  Dear Harvey,

  Thanks for your reply. I am seriously considering joining FOM when I
  get back to the U.S. and email is less of a pain to manage. I am not
  particularly good at speaking at forums where I don't know who the
  audience is, but I'll try.  Feel free to post whatever I send you
  (concerning FOM) till then.

  Best,			Steffen
  
  *****************************************************************
  
  Office address: Prof. Steffen Lempp
  		Department of Mathematics
  		University of Wisconsin
  		480 Lincoln Drive
  		Madison, WI 53706-1388   USA
  Office phone:   (608) 263-1975 or (608) 263-3054
  Office fax:     (608) 263-8891
  WWW home page:  http://www.math.wisc.edu/~lempp
  
  *****************************************************************

  -----
  
  From: Stephen G Simpson <simpson at math.psu.edu>
  To: Steffen Lempp <lempp at math.wisc.edu>
  Cc: Harvey Friedman <friedman at math.ohio-state.edu>
  Subject: Re: your comments on FOM
  Date: Tue, 11 Aug 1998 13:01:08 -0400 (EDT)
  
  Dear Steffen,
  
  This discussion about issues and programs in recursion theory is
  getting really good.  I want to continue it publicly, and I want to
  draw in more people in addition to you and me and Harvey.  Have you
  talked to people like Soare, Shore, Lerman, and Slaman about it?
  Would you consider doing so?
  
  Where shall we carry on the discussion?  I think the FOM list is an
  ideal forum, because the scope there is fairly broad.  Another
  possibility would be to use Peter Cholak's computability theory
  list, but that list seems to be dormant, and anyway the focus there
  is too narrow.
  
  [ three paragraphs omitted ]

   > I am not particularly good at speaking at forums where I don't know
   > who the audience is, but I'll try.
  
  The subscriber lists are available on the FOM web page at
  http://www.math.psu.edu/simpson/fom/, or I could e-mail them to you.
  
  Best regards,
  -- Steve