 One can also go further: instead of translating the identity relation  =  into something more complex, we may keep the language simple and complicate the interpretation.   We would like to replace “pointed graph” by “≡-class of pointed graph”. Since these are not sets, we instead employ Scott’s trick and instead use “set of  well-founded pointed graphs whose node sets are  ≡-equivalent and with the property that no pointed graph of smaller rank is  also  ≡-equivalent to them.” 