  Fortunately, even a rough description of the model-theoretic interpretation is enough to show that no such “close ties” exist. The model-theoretic interpretation is obtained by letting the significance of “∈” be fixed by the interpretation function of M, letting the quantifiers in Ω(x) range over the domain of M, and letting the significance of “=” and the propositional connectives be fixed by the recursion clauses in the the definition of first-order satisfaction. This description highlights two immediate differences between the model-theoretic interpretation and the ordinary English interpretation.