ABSTRACT
The various semantical meta-languages developed in the preceding chapters have one important feature in common, namely, that they contain in one way or another the whole of the object-language L to which they are applied. One way of achieving this is to require, as we have seen, that each symbol of the object-language have a corresponding translation within the semantical meta-language. Or we can think of the semantical meta-language as simply an extension of the object-language, achieved by the addition of certain syntactical and semantical primitives together with axioms characterizing them. But in either case, the object-language L reappears in toto within the semantical meta-language. We may speak of any such semantical meta-language as a translational meta-language, and the semantics involved as a translational semantics. All semantical meta-languages which have heretofore been studied in any technical detail in this book or elsewhere, seem to be translational in character.
