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AN APPLICATION OF RECURSION THEORY TO ANALYSIS
- Part of
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- Journal:
- Bulletin of Symbolic Logic / Volume 26 / Issue 1 / March 2020
- Published online by Cambridge University Press:
- 11 June 2020, pp. 15-25
- Print publication:
- March 2020
-
- Article
- Export citation
-
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].
