Paul-Elliot Anglès d'Auriac, Takayuki Kihara
Published 2019-07-05Version 1
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 $\Sigma^1_1$-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma^1_1$-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 Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem.
On the structure of the Medvedev lattice
A Comparison of Pair and Triple Partition Relations
The Consistency of Arithmetic
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