# Definition:Cardinality of Structure

## Definition

Let $\mathcal A$ be a first-order structure.

Then the cardinality of $\mathcal A$, denoted $\left\vert{ \mathcal A }\right\vert$, is defined as:

$\left\vert{ \mathcal A }\right\vert := \left\vert{ A }\right\vert$

where $\left\vert{ A }\right\vert$ is the cardinality of the underlying set $A$.