4 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.GN2026
The lattice of smooth sublocales as a Bruns-Lakser completion
Igor Arrieta, Anna Laura Suarez
We characterise the frame morphisms that lift to frame maps , where is the collection of joins of comp…
math.GN2025
Joins of closed sublocales are not always a coframe
Igor Arrieta
Given a locale , the collection of joins of closed sublocales forms a frame--somewhat unexpectedly, as it is naturally embedded in the coframe of all sublocale…
math.GN2024
The DeMorganization of a locale
Igor Arrieta
In 2009, Caramello proved that each topos has a largest dense subtopos whose internal logic satisfies De Morgan law (also known as the law of the weak excluded middle). This findin…