Tarski's hierarchy of metalanguages establishes that a coherent semantics requires object-language expressions to be named by distinct metalanguage terms, never by co-level expressions.
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A language or formal system used to talk about another language or formal system — in this context, the capacity within mathematics to refer to mathematical statements, syntax, proof, and truth.
object-language(Davidsonian theory of meaning)
The language to which a theory of meaning applies
semantics(Distinguished from metasemantics and pragmatics in Kaplan 1989)
The domain that concerns the facts about what meanings words or phrases have.