 Structuralism in this sense (for other kinds of structuralism, see, e.g., Hellman 2001) seems to fit well into the second-order logic framework. Contrary to set theory, second-order logic always assumes an underlying (limited) structure which is supposed to reflect one particular aspect of mathematics such as the semi-ring of natural numbers, the ordered field of real numbers, the field of complex numbers, the well-ordered structure \((\omega_1,&lt;)\), and so on. Ideally, these underlying structures are second-order characterizable. This leads to a problem with universal truths such as validity, but also with less complex ones such as the statement that every linear order has a completion, or that every field has an algebraic closure. Such universal truths are not about any particular structure.