 This understanding of the geometric terms as susceptible of multiple interpretations enables one to see the geometric sentences themselves, and sets of them, as providing definitions of a certain kind, a kind typically referred to as “implicit definition”. Specifically: A set AX of sentences containing n reinterpretable terms implicitly defines an n-place relation \(R_{\textit{AX}}\) holding of just those n-tuples which, when taken respectively as the interpretations of AX’s reinterpretable terms, render the members of AX true. (For example: if AX is the set {There are at least two points; Every point lies on at least two lines}, then \(R_{\textit{AX}}\) is the relation that holds of any triple \(\langle P, \textit{LO}, L\rangle\) such that P has at least two members, L has at least two members, and LO is a relation that holds between each member of P and at least two members of L.) The defined relation is simply the abstract structure, or as Hilbert puts it the “scaffolding”, shared by any such  n-tuple.[5] 