The Received View on Scientific Theories as developed by Carnap, Hempel, and others always had a philosophically motivated semantics. This semantics was given a Tarskian formalization by Kemeny and especially Przełęcki. Carnap's version of the semantics assumes a fixed domain and a restriction of the interpretations of observable terms to observable objects. Both assumptions are essential for his application of the Ramsey sentence and his criteria of analyticity. Przełęcki makes neither of the two assumptions and accordingly relies on modified criteria of analyticity. I argue for Carnap's restriction on interpretations of observational terms  and for Przełęcki's assumption of a variable domain and I provide accordingly modified criteria of analyticity that also allow for vague terms. Identifying the class of observable objects with the union of the extensions of observable terms then allows for a vague class of observable objects. To accommodate the resulting semantics, the criteria of analyticity can be generalized so that they can be expressed using only the concepts of set theory, states of systems, and empirical equivalence.