Structure notation - semicolon after carrier set?

Question

A structure is a carrier set together with some relation, functions, and constants on that set. If $A$ is the carrier set and $R, \dots, f, \dots, c, \dots$ are the relations, functions and constants, then we write $$\mathcal A=(A;R, \dots, f, \dots, c, \dots)$$ for the structure. Why do some authors (like I did here) put a semicolon after the carrier set but not in between the relations, functions and constants?

Answer 1

Quoting Wikipedia, a structure can be defined as a triple $\mathcal{A} = (A, \sigma, I)$ consisting of a domain $A$, a signature $\sigma$, and an interpretation function $I$ that indicates how the signature is to be interpreted on the domain. Thus in your notation, the semicolon is used to separate the domain from the interpretation (the signature is implicit).