The major results of this dissertation are theorems to the effect that certain classes of relational structures are not axiomatizable by universal sentences. Some of the particular classes considered are theories of measurement in the sense of the Scott-Suppes definition while others are theories of measurement according to a natural generalization of the above definition. Part of the significance of the results is that they are closely related to problems of proving representation theorems in measurement theory. Ideally, one would like to have a finite list of universal axioms which are both necessary and sufficient for guaranteeing the particular representation in which one is interested. The results of this technical report show that in many cases we are forced to settle for more modest achievements. Some intuitive statements of results whose precise formulations appear in the thesis are presented on (1) Additive Conjoint Measurement, (2) First-Order Segment of Decision Theory, (3) Difference Systems of Measurement, and (4) Multidimensional Scaling. (RP)