5 papers
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…
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…
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…
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…
Localic separation and the duality between closedness and fittedness
Igor Arrieta
There are a number of localic separation axioms which are roughly analogous to the -axiom from classical topology. For instance, besides the well-known subfitness and fitness,…