Let $\tau$ be a signature. A $\tau$ structure $\mathcal{A}$ comprises of a set $A$ called the universe (or domain) of $\mathcal{A}$ and an interpretation of the symbols of $\tau$ as follows:

• for each constant symbol $c\in\tau$ an element $c^A\in A$
• for each $n$ ary function symbol $f\in\tau$ a function $f^A:A^n\rightarrow A$
• for each $n$ ary relation symbol $R\in\tau$ a subset $R^A\subseteq A^n$

If $\mathcal{A}$ is a structure, then the cardinality (or power) of $\mathcal{A}$ $|\mathcal{A}|$ is the cardinality of its universe $A$