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The Medvedev lattice of computably closed sets
2005
Archive for Mathematical Logic
Simpson introduced the lattice P of Π 0 1 classes under Medvedev reducibility. Questions regarding completeness in P are related to questions about measure and randomness. We present a solution to a question of Simpson about Medvedev degrees of Π 0 1 classes of positive measure that was independently solved by Simpson and Slaman. We then proceed to discuss connections to constructive logic. In particular we show that the dual of P does not allow an implication operator (i.e. that P is not a
doi:10.1007/s00153-005-0278-y
fatcat:mgcvkwzke5er3efbkn5hvz23wi