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arXiv · 1307.0160

Infinite computations with random oracles

Merlin Carl·Philipp Schlicht
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Abstract

We consider the following problem for various infinite time machines. If a real is computable relative to 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 from ZFC for ordinal time machines (OTMs) with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider, infinite time Turing machines (ITTMs), unresetting and resetting infinite time register machines (wITRMs, ITRMs), and \alpha-Turing machines for countable admissible ordinals \alpha.

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Merlin Carl, Philipp Schlicht. 2013-06-29. Infinite computations with random oracles. https://doi.org/10.1215/00294527-383885

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