property of a Chu space

A property of a Chu space over $\mathrm{\Sigma }$ with carrier $𝒜$ is some $Y\subseteq {\mathrm{\Sigma }}^{𝒜}$. We say that a Chu space $𝒞=(𝒜,r,𝒳)$ satisfies $Y$ if $X\subseteq Y$.

For example, every Chu space satisfies the property ${\mathrm{\Sigma }}^{𝒜}$.