Definition

semialgebra

a class $\mathcal{S}$ of subsets of $\Omega$ is a semialgebra if

1. $\emptyset, \Omega \in \mathcal{S}$
2. $\mathcal{S}$ is a $\pi$-system
3. if $A \in \mathcal{S}$ then there is a finite collection of disjoint sets $C_1, \dots, C_n$ with $C_i \in \mathcal{S}, i = 1, \dots, n$ such that $A^{\complement} = \Sigma_{i=1}^{n}C_i$

mnemonic: an everything-nothing $\pi$-system in which complements are finite-disjointly decomposable