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AN APPLICATION OF RECURSION THEORY TO ANALYSIS

Published online by Cambridge University Press:  11 June 2020

LIANG YU*
Affiliation:
DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY NANJING 210093, P.R. CHINA E-mail: [email protected]

Abstract

Mauldin [15] proved that there is an analytic set, which cannot be represented by $B\cup X$ for some Borel set B and a subset X of a $\boldsymbol{\Sigma }^0_2$ -null set, answering a question by Johnson [10]. We reprove Mauldin’s answer by a recursion-theoretical method. We also give a characterization of the Borel generated $\sigma $ -ideals having approximation property under the assumption that every real is constructible, answering Mauldin’s question raised in [15].

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Articles
Copyright
© The Association for Symbolic Logic 2020

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