There is someone who is not in relation with himself but who is in relation with someone in relation with himself (so the first someone cannot be the second someone), not in relation with him

Model Theory

Categoricty

J.Corcoran, “Categoricity”, History and Philosophy of Logic, 1 (1980), pp.187-207.

Formulation / Formalization of the 4th Logical Notions

Non-axiomatizability of identity in FoLoWoE

W.Hodges, “Elementary predicate logic”, in D.Gabbay and F.Guenthner, Handbook of Philosophical logic, vol. I, Dordrecht, Reidel, 1983, pp.1-131.