linguistic:translation, structural:summarization, structural:reformatting, structural:scholar_edition, information:highlighting
Signature

The signature σ = (S, ar) {\displaystyle \sigma =(S,\operatorname {ar})} of a structure consists of:

The natural number n = ar (s) {\displaystyle n=\operatorname {ar} (s)} of a symbol s {\displaystyle s} is called the arity of s {\displaystyle s} because it is the arity of the interpretation of s. {\displaystyle s.}

Since the signatures that arise in algebra often contain only function symbols, a signature with no relation symbols is called an algebraic signature. A structure with such a signature is also called an algebra; this should not be confused with the notion of an algebra over a field.