# Definition:Standard Structure

## Definition

The structure $\left[{A,R}\right]$ is called a standard structure iff:

$\displaystyle R = \Epsilon \cap \left({ A \times A }\right)$ where $\Epsilon$ denotes the epsilon relation and $\times$ denotes the Cartesian product.

With a standard structure, $\left[{A,R}\right] \models p$ shall be abbreviated:

$\displaystyle A \models p \iff \left[{A , E \cap \left({ A \times A }\right)}\right] \models p$