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

Exercices de style: A homotopy theory for set theory II