The classical and non-classical theories both include and extend the minimal theory. They include it because every thesis of the minimal theory is also a thesis of the classical and non-classical ones: in the minimal, classical and non-classical theories, identity is symmetric, transitive, and weakly reflexive; identicals are indiscernible, and self-identical indiscernibles are identical. They extend it because the classical and non-classical theories each have theses that are not theses of the minimal theory. In the classical but not the minimal theory, identity is strongly reflexive and indiscernibles are identical; in the non-classical but not the minimal theory, identity is non-reflexive and some indiscernibles are not identical. 

C-complexes in C provide a model for the minimal theory: a domain in which identity is symmetric (T13), transitive (T14), and weakly reflexive (T12), identicals are indiscernible (T15#), and self-identical indiscernibles are identical (T16#). C-complexes in C+ provide a model for the classical theory: a domain in which identity is symmetric, transitive, and strongly reflexive (T26), identicals are indiscernible, and indiscernibles are identical (T27#). Finally, C-complexes in C- provide a model for the non-classical theory: a domain in which identity is symmetric, transitive, and non-reflexive (T26'), identicals are indiscernible, and some indiscernibles are not identical (T27'#). C-complexes may thus be taken as the values of particular variables in each of the aforementioned theories,²⁰ and C, C+ and C- may be enriched, as in the theory P and its extensions, by treating C-complexes as particulars.²¹