  This is the second part of a work initiated in \cite{GaHa}, where we
constructed a model category, $\Qt$, for set theory. In the present paper we
use this model category to introduce homotopy-theoretic intuitions to set
theory. Our main observation is that the homotopy invariant version of
cardinality is the covering number of Shelah's PCF theory, and that other
combinatorial objects, such as Shelah's revised power function - the cardinal
function featuring in Shelah's revised GCH theorem - can be obtained using
similar tools. We include a small "dictionary" for set theory in $\QtNaamen$,
hoping it will help in finding more meaningful homotopy-theoretic intuitions in
set theory.
