Taming Koepke's Zoo.

For ordinals alpha and ss, Koepke defined (alpha,ss)-Turing machines as Turing machines with tape length alpha and working time bounded above by ss. So far, their computational strength was determined for alpha = ss exponentially closed, alpha = ss = On and (alpha,ss) = (omega, On). In this paper, we determine the set of (alpha, ss)-writable subsets of a when a is multiplicatively closed and ss > alpha is admissible. This answers some open questions by Koepke in [5].