Q-Sets, Δ-Sets, and L-Spaces

The question whether there is a Lindelof Q-set space or Lindelof $\mathrm{\Delta }$-set space is considered. We show that J. Moore’s ZFC $L$-space is not a Q-set space in ZFC and, assuming all Aronszajn trees are special, it is not a $\mathrm{\Delta }$-set space.