FOM: Natural examples and evolution of subjects

[Joe Shipman]

Thanks, Harvey, for two very thought-provoking posts.  An observation
and a comment:

1) It seems a little unfair to restrict your domain for "naturalness" to
sets of integers so that you can say that there are no naturally
occuring examples of r.e. sets that are not recursive.  There are
certainly some naturally occurring sets of FINITE OBJECTS which are r.e.
but not recursive (integer polynomials with a zero, piecewise linear
spaces homeomorphic to the 5-sphere, presentations of the trivial
group).  It's bad enough that there is essentially only ONE canonical
example.

2) I agree that the four traditional branches of mathematical logic,
considered as individual subjects, are not at stage six yet; but can you
provide an example of a mathematical field which is?  (Even better would
be two examples, one where the stage six status is deserved and one
where it is undeserved.)

-- Joe