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A COMPARISON OF VARIOUS ANALYTIC CHOICE PRINCIPLES

Part of: Computability and recursion theory General logic

Published online by Cambridge University Press:  08 June 2021

PAUL-ELLIOT ANGLÈS D’AURIAC  and
TAKAYUKI KIHARA
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
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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 Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

Keywords

Weihrauch reducibilityarithmetical transfinite recusionΣ¹1-choice

MSC classification

Primary: 03D30: Other degrees and reducibilities
Secondary: 03D55: Hierarchies 03B30: Foundations of classical theories (including reverse mathematics)
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 4 , December 2021 , pp. 1452 - 1485
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Copyright
© Association for Symbolic Logic 2021

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