Journal of Symbolic Logic


Sy-David Friedman and P. D. Welch

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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 Σn rule. Such machines either halt or enter an infinite loop by stage ζ(n) =df μ ζ(n) [∃ Σ(n) > ζ(n) Lζ(n)Σn LΣ(n)], again generalising precisely the ITTM case.

The collection of such machines taken together computes precisely those reals of the least model of analysis.

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J. Symbolic Logic, Volume 76, Issue 2 (2011), 620-636.

First available in Project Euclid: 19 May 2011

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Friedman, Sy-David; Welch, P. D. Hypermachines. J. Symbolic Logic 76 (2011), no. 2, 620--636. doi:10.2178/jsl/1305810767.

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