Wille U
Jelmoli AG
J Math Psychol. 2000 Dec;44(4):617-650. doi: 10.1006/jmps.2000.1326.
This paper examines, in the scope of representational measurement theory, different axiomatizations and axiomatizability of linear and bilinear representations of ordinal data contexts in real vector spaces. The representation theorems proved in this paper are modifications and generalizations of Scott's characterization of finite linear measurement models. The advantage of these representation theorems is that they use only finitely many axioms, the number of which depends on the size of the given ordinal data context. Concerning the axiomatizability, it is proved by model-theoretic methods that finite linear measurement models cannot be axiomatized by a finite set of first order axioms. Copyright 2000 Academic Press.
本文在表征测量理论的范围内，研究了实向量空间中序数数据上下文的线性和双线性表示的不同公理化及其可公理化性。本文证明的表示定理是对斯科特有限线性测量模型特征的修改和推广。这些表示定理的优点在于它们仅使用有限多个公理，公理的数量取决于给定序数数据上下文的大小。关于可公理化性，通过模型论方法证明了有限线性测量模型不能由一组有限的一阶公理进行公理化。版权所有2000，学术出版社。
