Monadic stability versus structural nowhere denseness

Determine whether the notions of monadic stability and structural nowhere denseness coincide.

Background

The paper discusses near-linear type-count bounds for monadically stable classes and notes that a generalization to formulas with tuples of object and parameter variables would follow from the conjectured equivalence between monadic stability and structural nowhere denseness.

References

This conjecture would be implied by the conjecture that the notions of monadic stability and structural nowhere denseness coincide.

— On the generalized coloring numbers  (2501.08698 - Siebertz, 15 Jan 2025) in Section 8.1, 'VC-dimension and number of types'