In the antecedent ‘(∧Z &amp; U)X (∈f)’ is an abbreviation for the results from writing out the axioms of Zermelo set theory with all quantifiers relativized to the second order variable X, replacing each occurrence of the membership symbol ‘∈’ with the two place relation variable ‘f’. According to the applied mathematical statement, if there were structures satisfying the conjunction of the axioms of Zermelo set theory Z including some non-mathematical objects referred to in U, A would hold in such structures. The application statement A expresses the relations in questions, such as an isomorphism or a homomorphism between a physical system and certain set theoretic structures. This is the hypothetical component interpreted to express which relations would hold between certain mathematical structures (formulated as structures of ∧Z) and the entities studied in the world (the Urelemente).