5 papers
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
Mai Gehrke, Tomas Jakl, Luca Reggio
We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on…
On the axiomatisability of the dual of compact ordered spaces
Marco Abbadini, Luca Reggio
We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an Aleph_1-ary variety of algebras. Further, we s…
A characterisation of the category of compact Hausdorff spaces
Vincenzo Marra, Luca Reggio
We provide a characterisation of the category KH of compact Hausdorff spaces and continuous maps by means of categorical properties only. To this aim we introduce a notion of filtr…
Codensity, profiniteness and algebras of semiring-valued measures
Luca Reggio
We show that, if S is a finite semiring, then the free profinite S-semimodule on a Boolean Stone space X is isomorphic to the algebra of all S-valued measures on X, which are finit…
The Schützenberger product for syntactic spaces
Mai Gehrke, Daniela Petrisan, Luca Reggio
Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers…