The introduction of isomorphism in this context comes, of course, from the need to accommodate the preservation of structure between the (applied) mathematical part of the domain under study and the non-mathematical part. This holds in the crucial case in which the preservation of the synthetic properties and relations (S-isomorphism) by f leads to the preservation of the analytic applied mathematical relations (V-isomorphism) of the overall theory T′. It should be noted that the ‘synthetic’ structure is not meant to ‘capture’ the full structure of the mathematical theory in question, but only its applied part. (Recall that Hellman started with an applied mathematical theory T.)