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EXPANDING THE REALS BY CONTINUOUS FUNCTIONS ADDS NO COMPUTATIONAL POWER
Published online by Cambridge University Press: 26 September 2022
Abstract
We study the relative computational power of structures related to the ordered field of reals, specifically using the notion of generic Muchnik reducibility. We show that any expansion of the reals by a continuous function has no more computing power than the reals, answering a question of Igusa, Knight, and Schweber [7]. On the other hand, we show that there is a certain Borel expansion of the reals that is strictly more powerful than the reals and such that any Borel quotient of the reals reduces to it.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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