FOM: Lempp/Friedman correspondence; where are the recursion theorists?
Stephen G Simpson
simpson at math.psu.edu
Tue Aug 11 13:57:15 EDT 1998
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
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