English

The Borel monadic theory of order is decidable

Logic 2026-03-10 v2

Abstract

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

Keywords

Cite

@article{arxiv.2410.00887,
  title  = {The Borel monadic theory of order is decidable},
  author = {Sven Manthe},
  journal= {arXiv preprint arXiv:2410.00887},
  year   = {2026}
}