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A COMPARISON OF VARIOUS ANALYTIC CHOICE PRINCIPLES

Published online by Cambridge University Press:  08 June 2021

PAUL-ELLIOT ANGLÈS D’AURIAC
Affiliation:
L ACL, DÉPARTEMENT D’INFORMATIQUE FACULTÉ DES SCIENCES ET TECHNOLOGIE 61 AVENUE DU GÉNÉRAL DE GAULLE94010CRÉTEIL CEDEX, FRANCEE-mail: panglesd@lacl.fr
TAKAYUKI KIHARA
Affiliation:
DEPARTMENT OF MATHEMATICAL INFORMATICS GRADUATE SCHOOL OF INFORMATICS NAGOYA UNIVERSITY, JAPANE-mail: kihara@i.nagoya-u.ac.jp

Abstract

We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing a 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 Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

Type
Article
Copyright
© Association for Symbolic Logic 2021

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