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AN APPLICATION OF RECURSION THEORY TO ANALYSIS

Part of: Classical measure theory Set theory Computability and recursion theory Connections with other structures, applications

Published online by Cambridge University Press:  11 June 2020

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

Keywords

hyperarithmeticanalytic setsKurtz-randomnessσ-idea

MSC classification

Primary: 03D30: Other degrees and reducibilities
Secondary: 03D32: Algorithmic randomness and dimension 03D80: Applications of computability and recursion theory 03E15: Descriptive set theory 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 26 , Issue 1 , March 2020 , pp. 15 - 25
Copyright
© The Association for Symbolic Logic 2020

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