Minimal Kakeya subset

Determine whether every Borel Kakeya set contains a minimal Kakeya subset.

Background

A minimal Kakeya set is one with no proper Kakeya subset. The question concerns whether such a minimal object must occur inside every Borel Kakeya set.

References

Does every Borel Kakeya set $A$ contain a minimal Kakeya set $B\subseteq A$?

— Open Problems in Mathematical Logic  (2608.26628 - Barmpalias et al., 27 Aug 2026) in Section 4