The borel classes of mahler’s a, s, t, and u numbers

In this article we examine the A, S, T, and U sets of Mahler's classification from a descriptive set theoretic point of view. We calculate the possible locations of these sets in the Borel hierarchy. A turns out to be - complete, while U provides a rare example of a natural Incomplete set- We produce an upperbound of Lj for S and show that T. Our main result is based on a deep theorem of Schmidt that allows us to guarantee the existence of the T numbers.