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arXiv · 2410.00887

The Borel monadic theory of order is decidable

Sven Manthe
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Abstract

The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof extends to larger classes of sets.

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Sven Manthe. 2024-10-01. The Borel monadic theory of order is decidable. https://arxiv.org/abs/2410.00887

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