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Hypermachines

Published online by Cambridge University Press:  12 March 2014

Sy-David Friedman  and
P. D. Welch
Sy-David Friedman
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Währingerstraβe 25, 1090 Vienna, Austria, E-mail: sdf@logic.univie.ac.at
P. D. Welch
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK, E-mail: p.welch@bristol.ac.uk
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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 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 620 - 636
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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