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Hypermachines

  • Sy-David Friedman (a1) and P. D. Welch (a2)
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.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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