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June 2011 Hypermachines
Sy-David Friedman, P. D. Welch
J. Symbolic Logic 76(2): 620-636 (June 2011). DOI: 10.2178/jsl/1305810767

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. Wegive 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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Sy-David Friedman. P. D. Welch. "Hypermachines." J. Symbolic Logic 76 (2) 620 - 636, June 2011. https://doi.org/10.2178/jsl/1305810767

Information

Published: June 2011
First available in Project Euclid: 19 May 2011

zbMATH: 1220.03040
MathSciNet: MR2830419
Digital Object Identifier: 10.2178/jsl/1305810767

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 2 • June 2011
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