This paper on <a href="http://mishap.sdf.org/by:gavrilovich-and-hasson/what:a-homotopy-theory-for-set-theory/Exercises_de_style_A_homotopy_theory_for_set_theory-II.pdf"> homotopy and set theory</a> seems to take this question seriously: if you restrict yourself to posetal categories and try to do model categories in a brute-force naive way, you arrive to definitions of some set-theoretic invariants...So maybe we can say that Shelah is a computer. ;)