  We observe that the notion of two sets being equal up to finitely many
elements is a homotopy equivalence relation in a model category, and suggest a
homotopy-invariant variant of Generalised Continuum Hypothesis about which more
can be proven within ZFC and which first appeared in PCF theory. The formalism
allows to draw analogies between notions of set theory and those of homotopy
theory, and we indeed observe a similarity between homotopy theory
ideology/yoga and that of PCF theory. We also briefly discuss conjectural
connections with model theory and arithmetics and geometry.
