On qualitative axiomatizations for probability theory

In the literature, there are many axiomatiaations of qualitative probability. They all suffer certain defects: either they are too nonspecific and allow nonunique quantitative interpretations or am overspecific and rule out cases with unique quantitative interpretations. In this paper, it is shown that the class of qualitative probability structures with nonunique quantitative interpretations is not fiit order axiomatiaable and that the class of qualitative probability structures with a unique quantitative interpretation is not a flmite, fust order extension of the theory of qualitative probability. The idea behind the method of proof is quite general and can be used in other measurement situations.