 Almost anything from a concert hall to a kinship system can be referred to as a “structure”. So the first task for a structuralist account of representation is to articulate what notion of structure it employs. A number of different notions of structure have been discussed in the literature (for a review see Thomson-Jones 2011), but by far the most common is the notion of structure one finds in set theory and mathematical logic. A structure \(\mathcal{S}\) in that sense (sometimes “mathematical structure” or “set-theoretic structure”) is a composite entity consisting of the following: a non-empty set \(U\) of objects called the domain (or universe) of the structure and an indexed set \(R\) of relations on \(U\) (supporters of the partial structures approach, e.g., Da Costa and French (2003) and Bueno, French, and Ladyman (2002), use partial \(n\)-place relations, for which it may be undefined whether or not some \(n\)-tuples are in their extension). This definition of structure is widely used in mathematics and logic. We note, however, that in mathematical logic structures also contain a language and an interpretation function, interpreting symbols of the language in terms of \(U\) (see for instance Machover 1996 and Hodges 1997), which is absent from structures in the current context. It is convenient to write these as \(\mathcal{S}= \langle U, R \rangle\), where “\(\langle \, , \rangle\)” denotes an ordered tuple.