The Borel monadic theory of order is decidable
Sven Manthe · arXiv (Cornell University) · 2024
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_σ$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof extends to larger classes of sets.