A comparison of various analytic choice principles

Journal of Symbolic Logic 86 (4):1452-1485 (2021)
  Copy   BIBTEX

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 Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,038

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Pigeonhole and Choice Principles.Wolfgang Degen - 2000 - Mathematical Logic Quarterly 46 (3):313-334.
Rigit Unary Functions and the Axiom of Choice.Wolfgang Degen - 2001 - Mathematical Logic Quarterly 47 (2):197-204.
Factors of Functions, AC and Recursive Analogues.Wolfgang Degen - 2002 - Mathematical Logic Quarterly 48 (1):73-86.
Moral Uncertainty and Value Comparison.Amelia Hick - 2018 - Oxford Studies in Metaethics 13.
Choice principles and constructive logics.David Dedivi - 2004 - Philosophia Mathematica 12 (3):222-243.
When Analytic Narratives Explain.Anna Alexandrova - 2009 - Journal of the Philosophy of History 3 (1):1-24.
Non-constructive Properties of the Real Numbers.J. E. Rubin, K. Keremedis & Paul Howard - 2001 - Mathematical Logic Quarterly 47 (3):423-431.
Rawls, equality, and democracy.C. Edwin Baker - 2008 - Philosophy and Social Criticism 34 (3):203-246.

Analytics

Added to PP
2022-04-08

Downloads
5 (#1,541,436)

6 months
2 (#1,200,830)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Algebraic properties of the first-order part of a problem.Giovanni Soldà & Manlio Valenti - 2023 - Annals of Pure and Applied Logic 174 (7):103270.

Add more citations

References found in this work

Density of the Medvedev lattice of Π0 1 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
Density of the Medvedev lattice of Π01 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
Continuous higher randomness.Laurent Bienvenu, Noam Greenberg & Benoit Monin - 2017 - Journal of Mathematical Logic 17 (1):1750004.

Add more references