Journal of Symbolic Logic

Hypermachines

Sy-David Friedman and P. D. Welch

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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 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.

Article information

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

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1305810767

Digital Object Identifier
doi:10.2178/jsl/1305810767

Mathematical Reviews number (MathSciNet)
MR2830419

Zentralblatt MATH identifier
1220.03040

Citation

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


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