 The “MT” in “MTValid\((F)\)” stresses the fact that model-theoretic validity is different from universal validity. The notion of a meaning assignment which appears in the description of universal validity is a very imprecise and intuitive notion, while the notion of a structure appearing in a characterization of model-theoretic validity is a fairly precise and technical one. It seems clear that the notion of a structure for Fregean formalized languages is minimally reasonable, in the sense that a structure models the power of one or several meaning assignments to make false (the logical form of) some sentence. As we will mention later, the converse property, that each meaning assignment's validity-refuting power is modeled by some structure, is also a natural but more demanding requirement on a notion of structure.