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Infinite computations with random oracles

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CARL, Merlin, Philipp SCHLICHT, 2013. Infinite computations with random oracles

@techreport{Carl2013Infin-25589, title={Infinite computations with random oracles}, year={2013}, author={Carl, Merlin and Schlicht, Philipp} }

Carl, Merlin eng 2014-01-13T14:17:33Z 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?<br />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 $\alpha$. 2013 Carl, Merlin Schlicht, Philipp Infinite computations with random oracles 2014-01-13T14:17:33Z terms-of-use Schlicht, Philipp

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