Infinite computations with random oracles
Logic
2017-10-18 v4
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.
Cite
@article{arxiv.1307.0160,
title = {Infinite computations with random oracles},
author = {Merlin Carl and Philipp Schlicht},
journal= {arXiv preprint arXiv:1307.0160},
year = {2017}
}