Small cardinals and the pseudocompactness of hyperspaces of subspaces of βω

We study the relations between a generalization of pseudocompactness, named (κ,M)-pseudocompactness, the countably compactness of subspaces of βω and the pseudocompactness of their hyperspaces. We show, by assuming the existence of c-many selective ultrafilters, that there exists a subspace of βω that is (κ,ω⁎)-pseudocompact for all κ