×

Measurement representations of ordered, relational structures with Archimedean ordered translations. (English) Zbl 0658.92025

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
PDFBibTeX XMLCite
Full Text: Numdam EuDML