FOM: comments on RT2 paper

Stephen G Simpson simpson at
Wed Oct 21 20:03:19 EDT 1998

To: Peter Cholak, Carl Jockusch, Ted Slaman
CC: FOM list, Steffen Lempp

Dear Peter, Carl, and Ted,

Carl sent me your paper on the reverse mathematics of RT(2).  It is
extremely impressive!

Why do you list my book as "in preparation"?  Carl at least knows that
it is in press and will appear next month.  The correct
reference is:

    Stephen G. Simpson, Subsystems of Second Order Arithmetic,
    Perspectives in Mathematical Logic, Springer-Verlag, 1998, XIV +
    445 pages, in press.

On page 2 of your paper you say: "results in recursion theory are
sometimes the forerunners of results in reverse mathematics."  I
understand your point, but I disagree somewhat.  The outlook of
recursion theory is very different from that of reverse mathematics,
and there is nothing inevitable about the transition.  The difference
is like night and day.  That's why I'm especially delighted to see
that *some* recursion theorists (you three, Shore, Downey, ...) are
getting caught up in the reverse mathematics revolution!

The precise relationships between recursion theory, constructivism,
and reverse mathematics have been examined much more thoroughly on the
FOM list.  See for example Harvey Friedman's posting of 2 Aug 1998
21:51:35 and mine of 18 Aug 1998 14:10:44.  

I would love to continue that discussion!  It's too bad that the
recursion theory community is boycotting FOM.  Yes, Carl and Peter and
a few other recursion theorists are subscribing, but few have posted
anything, and the currently active hard-core recursion theorists have
been virtually silent.  (A notable exception is Steffen Lempp, who for
a while at least was willing to engage in dialogue.)  It seems to me
that the recursion theorists are throwing away an opportunity to
explain their field to a significant segment of the outside world.

Best regards,
-- Steve

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