The Cameron–Liebler problem for sets

Cameron–Liebler line classes and Cameron–Liebler kk-classes in PG(2k+1,q)PG(2k+1,q) are currently receiving a lot of attention. Here, links with the Erdős–Ko–Rado results in finite projective spaces occurred. We introduce here in this article the similar problem on Cameron–Liebler classes of sets, and solve this problem completely, by making links to the classical Erdős–Ko–Rado result on sets. We also present a characterisation theorem for the Cameron–Liebler classes of sets.