TITLE: Is equality of terms for "real" numbers with roots, logarithm, exponential, sin, cos, and other trigonometric operations decidable with a Turing-machine?
QUESTION [7 upvotes]: If yes, how? Also, I know you can't do it for arbitrary statements about real numbers, but that's not what I'm asking, and by "real" numbers, I mean the numbers constructible from 1, -, /, and the operations mentioned in the title.
Also, I don't care about numbers that can't be constructed from said operations and constant.

REPLY [13 votes]: Assuming Schanuel's conjecture, the answer seems to be yes, according to Daniel Richardson, "How to recognize zero" J. Symbolic Comput 24 (1997), 627–645 (doi:10.1006/jsco.1997.0157, available here online), in which the author defines a set of numbers he calls "elementary", which is algebraically closed and closed under exponential, logarithm and trigonometric functions, and for which equality is decidable (again, assuming Schanuel's conjecture).