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A comparison of various analytic choice principles (1907.02769v1)
Published 5 Jul 2019 in math.LO and cs.LO
Abstract: We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice of $\Sigma1_1$-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma1_1$-choice principle on the integers. Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem.