Non-pathology and hereditary non-pathology of Qd-coloring ideals

Determine whether Q^d-coloring ideals are non-pathological and whether they are hereditarily non-pathological.

Background

The paper extends Q-colorings to arbitrary finite dimensions using Devlin types, producing Qd-coloring ideals. It explicitly asks whether these higher-dimensional ideals share the non-pathological behavior sought for Q-coloring ideals, including after restriction to positive sets.

References

Question 5.37. Are the Qd-coloring ideals non-pathological? Are they hereditarily non-pathological?

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Question 5.37, p. 32