Hypermachines

Publisher： Cambridge University Press

E-ISSN： 1943-5886|76|2|620-636

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.76, Iss.2, 2011-06, pp. : 620-636

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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 Σ2 Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σ n rule. Such machines either halt or enter an infinite loop by stage , again generalising precisely the ITTM case.