A $\sigma$-complete Boolean algebra is a Boolean algebra which is also a $\sigma$-complete lattice; that is, it is a poset with countable limits and colimits that is also cartesian closed and satisfies the law of excluded middle.
Assuming excluded middle, the set of truth values is a $\sigma$-complete Boolean algebra.
Assuming the limited principle of omniscience, the boolean domain is a $\sigma$-complete Boolean algebra.
Assuming excluded middle, any $\sigma$-algebra on a set $X$ is a $\sigma$-complete Boolean algebra.
Last revised on August 28, 2024 at 11:43:56. See the history of this page for a list of all contributions to it.