[FOM] Fwd: logical complexity of Schanuel's Conjecture

[Dave Marker]

Joe Shipman asked if Schanuel's Conjecture is equivalent to an
arithmetic statement.

Angus Macintyre in his preprint "Turing meets Schanuel" shows, among
other things,
that if there is a counterexample to Schanuel's Conjecture than there
is a counterexample with among the recursively coded complex numbers.
(This preprint will be part of the proceedings of the Logic Colloquium
held a couple of years ago
in Manchester)

This gives, I think, a Pi^0_3-statement equivalent to Schanuel's conjecture.

I think that with a couple of tricks you can improve this to obtain an
equivalent
Pi^0_2 statement.

I've posted a link to a sketch of this
      http://www.math.uic.edu/~marker/SC2.pdf

Dave

David Marker
LAS Distinguished Professor
Mathematics, Statistics, and Computer Science
University of Illinois at Chicago