I would like to understand exactly what is meant in a grammar discussion when someone uses the word "coreferential". I understand it to mean that two or more constituents (e.g. a noun and a noun phrase) must reference the same entity, but I'm not really sure what is required for a constituent to be considered a reference, as distinct from a description or an ascription.
Consider:
Jane Doe, soprano in the church choir, had a bad cold.
Jane Doe, a soprano in the church choir, had a bad cold.
Jane Doe, best soprano in the church choir, had a bad cold.
Jane Doe, the best soprano in the church choir, had a bad cold.
Are all of the bolded phrases coreferential with "Jane Doe"? Only two of them, the ones with the article, can clearly stand as the grammatical subject of the verb phrase in that sentence:
*soprano in the church choir had a bad cold.
*best soprano in the church choir had a bad cold. (marginal?)
a soprano in the church choir had a bad cold.
the best soprano in the church choir had a bad cold.
And of those two, only the latter, the one with the definite article, seems (to me) to yield meaning equivalent to the following:
Jane Doe had a bad cold.
So, to be "coreferential", does the noun phrase have to point directly to the preceding noun, to it uniquely, and be able to stand in its place in the sentence and yield equivalent meaning when so standing, or does it merely have to be predicable of the preceding noun?