Hypermachines
Sy‐David Friedman, PHILIP D. WELCH · Journal of Symbolic Logic · 2011
Abstract The Infinite Time Turing Machine model [8] of Hamkins and Kidder is, in an essential sense, a “Σ2-machine” in that it uses a Σ2Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σn rule. Such machines either halt or enter an infinite loop by stage , again generalising precisely the ITTM case. The collection of such machines taken together computes precisely those reals of the least model of analysis.