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

Dave Marker marker at math.uic.edu
Fri Oct 23 12:48:57 EDT 2015

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
Pi^0_2 statement.

I've posted a link to a sketch of this


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

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