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Inside the Muchnik degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions

2014
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Annals of Pure and Applied Logic
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It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π 0 1 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π 0 1 subsets of Cantor space, we show the existence of a finite-∆ 0 2 -piecewise degree containing infinitely many finite-(Π 0 1 ) 2 -piecewise degrees, and a finite-(Π 0 2 ) 2piecewise degree containing infinitely many finite-∆ 0 2

doi:10.1016/j.apal.2014.03.001
fatcat:xyn6jp6yureq3lql4hpfvcndbi