Infinite computations with random oracles

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2013
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Schlicht, Philipp
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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 ($OTM$s) with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite time Turing machines ($ITTM$s), unresetting and resetting infinite time register machines ($wITRM$s, $ITRM$s), and $\alpha$-Turing machines ($\alpha$-$TM$s) for countable admissible ordinals $\alpha$.

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510 Mathematik
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ISO 690CARL, Merlin, Philipp SCHLICHT, 2013. Infinite computations with random oracles
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@techreport{Carl2013Infin-25589,
  year={2013},
  title={Infinite computations with random oracles},
  author={Carl, Merlin and Schlicht, Philipp}
}
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    <dcterms:abstract xml:lang="eng">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?&lt;br /&gt;We show that the answer is independent from $ZFC$ for ordinal time machines ($OTM$s) with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite time Turing machines ($ITTM$s), unresetting and resetting infinite time register machines ($wITRM$s, $ITRM$s), and $\alpha$-Turing machines ($\alpha$-$TM$s) for countable admissible ordinals $\alpha$.</dcterms:abstract>
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