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

• Assuming the limited principle of omniscience, the boolean domain is a $\sigma$-complete Heyting algebra.

 Related concepts

• sigma-complete lattice

• sigma-frame

• sigma-complete Boolean algebra

• Heyting algebra

• complete Heyting algebra