Luce, R. D. Measurement representations of ordered, relational structures with Archimedean ordered translations. (English) Zbl 0658.92025 Math. Inf. Sci. Hum. 101, 35-47 (1988). By numerically representing empirical information - by measurement structures - the results, reported in a terse style and without comments and proofs, do not duplicate exactly those in the mathematical literature. What corresponds to Archimedeanness for a general ordered relational structure? When does a structure have a numerical representation that is unique up to subgroups of the affine transformations? When can a structure enter into a system of numerical measures that are interlocked as products of powers of each other? In the homogeneous case, there is a single answer: Define a translation to be either the identity or an automorphism with no fixed points, then the translations shall form a homogeneous Archimedean ordered group, where the order is the asymptotic one, defined in terms of the order of the structure. Reviewer: C. Cusmir MSC: 92F05 Other natural sciences (mathematical treatment) 06F15 Ordered groups 06F99 Ordered structures Keywords:representing empirical information; measurement structures; general ordered relational structure; affine transformations; translation; automorphism; homogeneous Archimedean ordered group PDFBibTeX XMLCite \textit{R. D. Luce}, Math. Inf. Sci. Hum. 101, 35--47 (1988; Zbl 0658.92025) Full Text: Numdam EuDML