Monotonic Access Structure
The access structure itself need not be non-empty, so the universe doesn't have to be in the structure. Of course, any non-empty access structure will have $\{1,2,\dots,n\}$ as an element.

In the context of ABE, it suffices to consider monotone access structures if the scheme supports an expressive policy set, because any subset $\mathbb{B}$ of $2^{\{1,2,\dots,n\}}$ (i.e., any not necessarily monotone access structure of universe $\{1,2,\dots,n\}$) can be encoded as a monotone access structure $\mathbb{A}$ of the universe $\{\pm1,\pm2,\dots,\pm n\}$ as follows:
$$\begin{aligned}\mathbb{A}'&amp;{}=\Bigl\{{\{i\,|\,i\in X\}\cup\{-j\,|\,j\notin X\}}\,\Big|\,X\in\mathbb{B}\Bigr\},\\\mathbb{A}&amp;{}=\Bigl\{A\,\Big|\,\mathbb{A}'\ni A'\subseteq A\subseteq\{\pm1,\pm 2,\dots,\pm n\}\Bigr\}.\end{aligned}$$
In English, this means you prepare positive/negative literals for every member of $\{1,2,\dots,n\}$, then encode any subset of it by explicitly putting negative literals for non-members into it, which gives you $\mathbb{A}'$. Then you take the smallest monotone access structure $\mathbb{A}$ containing $\mathbb{A}'$.

Monotone access structure gives rise to secret-sharing schemes, which are an important ingredient in many ABE constructions. Note that secret-sharing schemes can only handle monotone access structures, because gaining more shares only makes reconstruction easier.