UC Berkeley

This dissertation consists of four largely independent chapters. The first two chaptersconcern counterparts of classical theorems in modal logic in more general semantics: the Sahlqvist Correspondence Theorem inter alia for possibility semantics in Chapter 1 and the Goldblatt-Thomason Theorem and Fine’s Canonicity Theorem for neighborhood semantics in Chapter 2. Chapter 3 contains various results on Heyting algebras, among which is the topological-dynamical study of the automorphism group of the smallest existentially closed Heyting algebra. The last chapter establishes choice-free duality between the category of ortholattices and a category of certain spectral spaces.