kedst13+ at pitt.edu
Sat Sep 4 10:16:31 EDT 1999
>Kurtz and other recursion theorists are evading Friedman's main point.
>The point is that recursion theory is in need of reform, because the
>advanced theory of r.e. sets and degrees is almost entirely irrelevant
>to fundamental issues in f.o.m. and f.o.c.s.
Surely it's time to ask Simpson for a little more clarity on what is meant
here. What exactly is meant by 'a fundamental issue in f.o.m', and are
there examples of mature mathematical disciplines which regularly make
contributions to 'fundamental issues in f.o.m'? Obviously, reverse
mathematics is supposed to be such a mathematical discipline. However, in
spite of everything I've heard both Simpson and Friedman say about this
issue, I still don't see as clearly as I would like how reverse mathematics
fares any better than the theory of r.e. sets and degrees. Also - putting
reverse mathematics to the side, are there any other examples of mature
mathematical disciplines making such contributions?
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