Measurement structures with Archimedean ordered translation groups
The author focuses on three questions of generalizing properties of concatenation structures to ordered structures lacking any operation: 1. the natural generalization of the idea of Archimedeaness, of commensurability between large and small, 2. the natural generalization of the concept of a unit concatenation structure in which the translations (automorphisms with no fixed point) can be represented by multiplication by a constant, 3. the natural generalization of a ratio scale concatenation structure being distributive in a conjoint one, which has been shown to force a multiplicative representation of the latter and the product-of-powers representation of units found in physics. He proves (Theorem 5.1 and 5.2) that for homogeneous structures the latter two questions are equivalent to having the property that the set of all translations forms a homogeneous Archimedean ordered group. He explores a sufficient condition for Archimedeaness of the translations and suggests that Archimedean order of the translations is the answer to the first question.
scientific article; zbMATH DE number 4023357
scientific article