“A is necessarily B.”
That seems to be a reference to things; not to sentences or words. Thus Carnap offers this alternative:
“The statement ‘A is B’ is a necessary one.”
What's necessary in the above isn't the properties of things: it's the properties of sentences. Necessity is only a property of sentences (e.g., in conceptually analytic statements).
a = b
both a and b “are concepts of the same individual”; not variables for concrete objects. Thus perhaps we should write:
[Ca] = [Cb]
Thus if a and b are concepts of/for the same individual, we can create, from this, an analytic statement. That is, in the often-used example
“All bachelors are unmarried men.”
the words “bachelors” and “unmarried men” both refer or denote different concepts of the same set of individuals (i.e., they have the same extension).
i) “Bachelors are necessarily unmarried men.”
Thus i) is an example of de re necessity. It's a statement about concrete objects: bachelors and unmarried men. And ii), on the other hand, is an example of de dicto necessity: it's a statement about the concepts BACHELOR and UNMARRIED MAN.
(c) (Uc Bc)
However, that conditional (in which 'c' means concept) doesn't really capture necessity. Thus we can have a biconditional instead: