nLab sigma-complete Heyting algebra

Idea

A $\sigma$-complete Heyting algebra is a Heyting algebra which is also a $\sigma$-complete lattice; that is, it is a poset with countable limits and colimits that is also cartesian closed.

 Examples

• The set of truth values is a $\sigma$-complete Heyting algebra (even a complete Heyting algebra)

• The initial $\sigma$-complete Heyting algebra is the classifier of hyperarithmetical subsets. In the presence of the limited principle of omniscience, this is just the boolean domain.

 Related concepts

• sigma-complete lattice

• sigma-frame

• sigma-complete Boolean algebra

• Heyting algebra

• complete Heyting algebra