Pseudocomplement

Summary

Let $L$ be a lattice with a least element $0$, and let $a \in L$. The pseudocomplement of $a$ is the largest element whose meet with $a$ is $0$, when such an element exists. It is written $a^*$. In a Boolean algebra it is the usual complement, and in a Heyting algebra it is $a \to 0$. Pseudocomplements give a weak, intuitionistic form of negation.