  This brings us to a second point. Skolem's Paradox depends crucially upon the fact that we're using a first-order axiomatization of set theory. More precisely, it depends upon the fact that we're using first-order model theory to interpret this axiomatization. In 1930, Zermelo proved that (second-order) models of second-order ZFC compute cardinalities and power sets  correctly.[28]  In particular, then, if M is a model for second-order ZFC and if  mˆ  ∈ M, then M  ⊨  “mˆ  is uncountable” if and only  if {m | M  ⊨  m ∈  mˆ }  really is uncountable. Hence, Skolem's Paradox doesn't arise in the second-order context (Zermelo 1930; Shapiro 1991).