3 papers
math.LO2026
A topos for étale-finite Heyting algebras
Marco Abbadini, Rodrigo Nicolau Almeida, Igor Arrieta
A longstanding open problem is whether every Heyting algebra is the lattice of truth values (i.e., of subterminal objects) of some elementary topos. A positive answer is known for…
math.LO2025
Esakia order-compactifications and locally Esakia spaces
Rodrigo Nicolau Almeida, Guram Bezhanishvili, Nick Bezhanishvili
We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characte…
math.LO2024
Maximality Principles in Modal Logic and the Axiom of Choice
Rodrigo Nicolau Almeida, Guram Bezhanishvili
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known F…