Products of ∆-sets and Q-sets

Q-sets and ∆-sets are special subsets of the reals related to questions of normality and countable paracompactness. Every Q-set is trivially a ∆-set, and it is unknown whether the converse holds. In this talk, I will present two results on the productivity of ∆-sets that are closely analogous to results on Q-sets in the literature: (1) it is consistent that there exists a Q-set whose square is not a ∆-set; and (2) if there exists a ∆-set, then there exists another ∆-set all of whose finite powers are ∆-sets.