The Transfinite Action of 1 Tape Turing Machines

We produce a classification of the pointclasses of sets of reals produced by infinite time turing machines with 1-tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. We consider some relations of such classes with other similar notions, such as arithmetical quasi-inductive definitions. It is noted that the action of ω many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a → a″ The ordinals beginning gaps in the ”clockable” ordinals are admissible ordinals, and the length of such gaps corresponds to the degree of reflection those ordinals enjoy.