Abstract
By a theorem of Sacks, if a real \(x\) is recursive relative to all elements of a set of positive Lebesgue measure, \(x\) is recursive. This statement - and the analogous statement for non-meagerness instead of positive Lebesgue measure - has been shown to carry over to many models of transfinite computations in [7]. Here, we start exploring another analogue concerning recognizability rather than computability. We show that, for Infinite Time Register Machines (\(ITRM\)s), if a real \(x\) is recognizable relative to all elements of a non-meager Borel set \(Y\), then \(x\) is recognizable.
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Carl, M. (2015). \(ITRM\)-Recognizability from Random Oracles. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_14
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DOI: https://doi.org/10.1007/978-3-319-20028-6_14
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