2 citations · 8 across the 7 of their papers we have counts for
9 papers
Stone-Gelfand duality for metrically complete lattice-ordered groups
Marco Abbadini, Vincenzo Marra, Luca Spada
We extend Yosida's 1941 version of Stone-Gelfand duality to metrically complete unital lattice-ordered groups that are no longer required to be real vector spaces. This calls for a…
Relative ideals in homological categories, with an application to MV-algebras
Serafina Lapenta, Giuseppe Metere, Luca Spada
Let be a homological category and be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to , and we show that, un…
Are locally finite MV-algebras a variety?
Marco Abbadini, Luca Spada
We answer Mundici's problem number 3 (D. Mundici. Advanced Łukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equi…
Join-completions of ordered algebras
José Gil-Férez, Luca Spada, Constantine Tsinakis +1
We present a systematic study of join-extensions and join-completions of ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and co…
MV-algebras, infinite dimensional polyhedra, and natural dualities
Leonardo M. Cabrer, Luca Spada
We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify…
Canonical formulas for k-potent commutative, integral, residuated lattices
Nick Bezhanishvili, Nick Galatos, Luca Spada
Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionisti…
General affine adjunctions, Nullstellensätze, and dualities
Olivia Caramello, Vincenzo Marra, Luca Spada
We introduce and investigate a category-theoretic abstraction of the standard "system-solution" adjunction in affine algebraic geometry. We then look further into these geometric a…
Two isomorphism criteria for directed colimits
Vincenzo Marra, Luca Spada
Using the general notions of finitely presentable and finitely generated object introduced by Gabriel and Ulmer in 1971, we prove that, in any (locally small) category, two sequenc…
Representation of Perfect and Local MV-algebras
Brunella Gerla, Ciro Russo, Luca Spada
We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Ab…