Abstract
This chapter covers the fundamentals of Heyting algebras and closure algebras, as well as their connections to superintuitionistic logics and modal systems. Characterizations of the congruences of Heyting algebras and closure algebras are given in terms of filters and skeletal filters, respectively. The notion of a skeletal closure algebra is introduced. Functors between the categories of Heyting algebras and closure algebras are described, establishing an equivalence between the categories of Heyting algebras and skeletal closure algebras. Finally, the rank of an element of a closure algebra is defined, and the skeletal closure algebras are characterized as those closure algebras all of whose elements have finite rank.
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