[FOM] What is the logical complexity of Schanuel's conjecture?

[Joe Shipman]

Schanuel's Conjecture states that if a1, a2, ... , a_n are complex numbers that are linearly independent over the rationals, then adjoining them and their exponentials to the rationals gives a field with transcendence degree at least n.

Schanuel's conjecture has interesting arithmetical consequences, but is it equivalent to an arithmetical statement? If not, how low in the logical hierarchy of statements of second-order arithmetic can it or an equivalent statement be found?

-- JS

Sent from my iPhone