  In his seminal work on localisation of spectra, Ravenel initiated the study
of Bousfield classes of spectra related to the chromatic perspective. In
particular he showed that there were infinitely many distinct Bousfield classes
between $\langle MU\rangle$ and $\langle S^0\rangle$. The main topological goal
of this paper is investigate how these Bousfield classes are related to that of
another classical Thom spectrum $MSp$, and in particular how $\langle
MSp\rangle$ is related to $\langle MU\rangle$.
  We follow the approach of Ravenel, but adapt it using the theory of
$P$-algebras to give vanishing results for cohomology. Our work involves
dualising and considering comodules over duals of $P$-algebras; these ideas are
then applied to the mod~$2$ Steenrod algebra and certain subHopf algebras.
