5 papers · 1 filter
On the symmetry behind duality
Marco Abbadini, Achim Jung
Dualities such as Stone duality and the duality between sober spaces and spatial frames hinge on an interaction between open sets and compact saturated sets. In several important c…
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…
On the lack of colimits in various categories arising in pointfree topology and algebraic logic
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We prove that the category of McKinsey-Tarski algebras is not equivalent to a variety of algebras, thus answering a question of Peter Jipsen in the negative. More generally, we sho…
Unital Specker -groups and boolean multispaces
Marco Abbadini, Daniele Mundici
As a topological generalization of the notion of a multiset, a boolean multispace is a boolean space with a continuous function , where $\mathbb Z_…
Duality for finitely valued algebras
Marco Abbadini, Adam PÅenosil
The theory of natural dualities provides a well-developed framework for studying Stone-like dualities induced by an algebra which acts as a dualizing object when equip…