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COUNTABLY PERFECTLY MEAGER SETS
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 86 / Issue 3 / September 2021
- Published online by Cambridge University Press:
- 07 June 2021, pp. 1214-1227
- Print publication:
- September 2021
-
- Article
- Export citation
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We study a strengthening of the notion of a perfectly meager set. We say that a subset A of a perfect Polish space X is countably perfectly meager in X, if for every sequence of perfect subsets
$\{P_n: n \in \mathbb N\}$
of X, there exists an 
$F_\sigma $
-set F in X such that 
$A \subseteq F$
and 
$F\cap P_n$
is meager in 
$P_n$
for each n. We give various characterizations and examples of countably perfectly meager sets. We prove that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszyński.
