Theorem E

There is an effectively computable constant such that if is admissible of length , then all elements of have stopping time k except possibly the smallest element of S.

Proof E

(sketch). The results of A. Baker and N. I. Feldman on linear forms in logarithms of algebraic numbers ([10], Theorem 3.1) imply that there is an effectively computable absolute constant such that for all ,

Consequently there is an effectively computable absolute constant such that for one has

and (2.12) then yields

Since is admissible, , where by (2.11). Therefore

But all elements of except exceed and

for all sufficiently large k, so the theorem follows by (2.14).