â€¢ 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. â€¢ We consider some relations of such classes with other similar notions, such as arithmetical quasi-inductive definitions. â€¢ It is noted that the action of many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a a â€¢ 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.
Bibliographical notePublisher: Springer-Verlag, Berlin
Other identifier: IDS Number: BCP14