7 citations · 21 across the 16 of their papers we have counts for
16 papers
Formal squares over the unit square separate FS-domains from RB-domains
Marco Abbadini
Every RB-domain is an FS-domain. Whether the converse holds was a long-standing open problem. We prove that the domain of closed axis-parallel squares in the plane whose centres li…
The doctrinal Gödel's completeness theorem and the type space functor
Marco Abbadini, Francesca Guffanti
We give a self-contained proof of Gödel's completeness theorem entirely within the formalism of first-order Boolean doctrines (an algebraic approach to classical many-sorted first-…
On the Beck--Chevalley condition
Marco Abbadini, Francesca Guffanti
Boolean hyperdoctrines provide an algebraic semantics for classical first-order logic with equality. In the definition of a Boolean hyperdoctrine, the Beck--Chevalley condition cap…
The unification type of Lukasiewicz logic with a bounded number of variables
Marco Abbadini, Luca Spada
Building on the correspondence between finitely axiomatised theories in Łukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz…
On the axiomatisability of the dual of compact ordered spaces
Marco Abbadini
We prove that the category of Nachbin's compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of a…
Freely adding one layer of quantifiers to a Boolean doctrine
Marco Abbadini, Francesca Guffanti
We describe the layer of quantifier alternation depth at most one of the quantifier completion of a Boolean doctrine over a small category. This amounts to a doctrinal version of H…
Barr-coexactness for metric compact Hausdorff spaces
Marco Abbadini, Dirk Hofmann
Compact metric spaces form an important class of metric spaces, but the category that they define lacks many important properties such as completeness and cocompleteness. In recent…
Varieties of MV-monoids and positive MV-algebras
Marco Abbadini, Paolo Aglianò, Stefano Fioravanti
MV-monoids are algebras where is a bounded distributive lattice, both $\langle A, \oplus, 0…
Quantifier-free formulas and quantifier alternation depth in doctrines
Marco Abbadini, Francesca Guffanti
This paper aims to incorporate the notion of quantifier-free formulas modulo a first-order theory and the stratification of formulas by quantifier alternation depth modulo a first-…
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…
Barr-Exact Categories and Soft Sheaf Representations
Marco Abbadini, Luca Reggio
It has long been known that a key ingredient for a sheaf representation of a universal algebra A consists in a distributive lattice of commuting congruences on A. The sheaf represe…
A finite axiomatization of positive MV-algebras
Marco Abbadini, Peter Jipsen, Tomáš Kroupa +1
Positive MV-algebras are the subreducts of MV-algebras with respect to the signature . We provide a finite quasi-equational axiomatization for…
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…
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…
Equivalence à la Mundici for commutative lattice-ordered monoids
Marco Abbadini
We provide a generalization of Mundici's equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category of unital commutative lattice-ordered groups is equ…
The dual of compact ordered spaces is a variety
Marco Abbadini
In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially ordered spaces and monotone continuous maps is a quasi-variety…