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2017 Infinite Computations with Random Oracles
Merlin Carl, Philipp Schlicht
Notre Dame J. Formal Logic 58(2): 249-270 (2017). DOI: 10.1215/00294527-3832619

Abstract

We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and resetting infinite-time register machines, and α-Turing machines for countable admissible ordinals α.

Citation

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Merlin Carl. Philipp Schlicht. "Infinite Computations with Random Oracles." Notre Dame J. Formal Logic 58 (2) 249 - 270, 2017. https://doi.org/10.1215/00294527-3832619

Information

Received: 18 March 2014; Accepted: 21 August 2014; Published: 2017
First available in Project Euclid: 21 February 2017

zbMATH: 06751302
MathSciNet: MR3634980
Digital Object Identifier: 10.1215/00294527-3832619

Subjects:
Primary: 03D32, 03D60, 03D65
Secondary: 03E15, 03E35, 68Q05

Rights: Copyright © 2017 University of Notre Dame

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Vol.58 • No. 2 • 2017
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