nLab sigma-complete Boolean algebra

Idea

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.

 Examples

• 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.

 Related concepts

• sigma-complete lattice

• sigma-frame

• sigma-complete Heyting algebra

• Boolean algebra

• complete Boolean algebra

• sigma-algebra

• measurable space

• measure space

References

• Thierry Coquand, Jonas Höfer?, Hugo Moeneclaey, Model for Synthetic Stone Duality (draft pdf)