  A well-known version of Rowbottom's theorem for supercompactness ultrafilters
leads naturally to notions of two-cardinal Ramseyness and corresponding normal
ideals introduced herein. Generalizing results of Baumgartner [7, 8], Feng [22]
and the first author [16, 17], we study the hierarchies associated with a
particular version of two-cardinal Ramseyness and a strong version of
two-cardinal ineffability, as well as the relationships between these
hierarchies and a natural notion of transfinite two-cardinal indescribability.

Logic