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Sven Manthe: The Borel monadic theory of order is decidable
Автор: Hausdorff Center for Mathematics
Загружено: 2025-12-15
Просмотров: 41
Описание:
The monadic second-order theory of $(\mathbb{N}, ＜)$, S1S, is decidable (it essentially describes $\omega$-automata). Undecidability of the monadic theory of $(\mathbb{R}, ＜)$ was proven by Shelah. Previously, Rabin proved decidability if the monadic quantifier is restricted to $F \delta$-sets. We discuss decidability for Borel sets. Moreover, the Boolean combinations of $F \delta$-sets form an elementary substructure. Under determinacy hypotheses, the proof extends to larger classes of sets.
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