  First, the model-theoretic interpretation understands “∈” to refer to whatever binary relation on M happens to fall under the interpretation function of M; in contrast, the ordinary-English interpretation of Ω(x) understands “∈” to refer to the real set-theoretic membership relation. But there is no reason to think that these two understandings agree with each other. We can find cases were M  ⊨ m1 ∈ m2, despite the fact that neither m1 nor m2 are even sets (indeed, as far as the model theory is concerned, m1 and m2 could both be cats, or rabbits, or hedgehogs, or  …).[18]  Further, even when all of the elements in M are sets, this provides no guarantee that the model-theoretic understanding of “∈” will agree with the ordinary English understanding. We can find a case where m1 and m2 are genuine sets, but where M  ⊨ m1 ∈ m2, despite the fact that m1 is not really a member of m2; similarly, we can find a case where M  ⊨ m1 ∉ m2, despite the fact that m1 really is a member of m2 (and where, once again, m1 and m2 are genuine  sets).[19]