 Say that two interpretations \(M_1 =\langle d_1,I_1\rangle, M_2 =\langle d_2,I_2\rangle\) are equivalent if one of them is a submodel of the other, and for any formula of the language and any variable-assignment \(s\) on the submodel, \(M_1,s\vDash \theta\) if and only if \(M_2,s\vDash \theta\). Notice that if two interpretations are equivalent, then they satisfy the same sentences.