Stone topology on a type space
= Stone topology on a type space
{c}
{title2=$[\varphi]=\{p:\varphi\in p\}$}
For a <type space> $S_n^M(A)$, the basic open set $[\varphi]$ consists of complete types containing the formula $\varphi$. These sets are clopen, satisfy $[\varphi]\cap[\psi]=[\varphi\wedge\psi]$, and distinguish distinct types. The <compactness theorem> makes this topology compact; it is Hausdorff and has a basis of clopen sets.