This note investigates the Automatic Baire property in Cantor space, revealing limitations of finite subsets and implications of increased computational power.
Automatic Baire property is a variant of the usual Baire property which is fulfilled for subsets of the Cantor space accepted by finite automata. We consider the family [Formula: see text] of all subsets of the Cantor space having the Automatic Baire property. In particular we show that not all finite subsets have the Automatic Baire property, and that already a slight increase of the computational power of the accepting device may lead beyond the class [Formula: see text].
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Ludwig Staiger (2026) studied this question.
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