Bourbaki theory of isomorphism, examples of untransportable formulas
In their book "Theory of sets" Bourbaki suggested a general theory of isomorphism.
It seems that the Bourbaki theory can be greatly simplified if we allow only one principal base set. The example of an untransportable relation (i.e. formula) in the book involves 2 principal base sets.
Are there examples of untrasportable formulas when we allow only one principal base set?