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.

• Type: Conference
• Year: 2005
• Where: CIE
• Authors: Philip D. Welch
• Keywords: Arithmetical Quasi-inductive Definitions, CIE 2005, Time Turing Machines, Usual Turing Sense