  We prove a topological completeness theorem for the modal logic GLP
containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to
capture progressively stronger notions of consistency in mathematical theories.
We show that, given a scattered space $X$ of large-enough rank, any sentence
$\phi$ consistent with GLP can be satisfied in a polytopological space based on
the finitely many Icard topologies over $X$ that correspond to the finitely
many modalities appearing in $\phi$.
