\begin{definition}[Definition:Scott Sigma]
Let $L = \struct{S, \preceq}$ be an ordered set.
'''Scott sigma''' $\map \sigma L$ is a set of subsets of $S$ and equals to
:$\leftset {U \subseteq S: U}$ is upper and has property (S)$\rightset{}$
{{NamedforDef|Dana Stewart Scott|cat = Scott, Dana}}
\end{definition}