A comparison of various analytic choice principles

07/05/2019

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by   Paul-Elliot Anglès d'Auriac, et al.

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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 Σ^1_1-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the Σ^1_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 Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem.