27 citations · 86 across the 17 of their papers we have counts for
24 papers
The Intermediate Logic of Convex Polyhedra
Sam Adam-Day, Nick Bezhanishvili, David Gabelaia +1
We investigate a recent semantics for intermediate (and modal) logics in terms of polyhedra. The main result is a finite axiomatisation of the intermediate logic of the class of al…
Separable MV-algebras and lattice-groups
Vincenzo Marra, Matías Menni
General theory determines the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-…
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…
Polyhedral completeness of intermediate logics: the Nerve Criterion
Sam Adam-Day, Nick Bezhanishvili, David Gabelaia +1
We investigate a recently-devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally…
Priestley duality for MV-algebras and beyond
Wesley Fussner, Mai Gehrke, Sam van Gool +1
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice b…
The two-sorted algebraic theory of states, and the universal states of MV-algebras
Tomáš Kroupa, Vincenzo Marra
We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian…
Orders on groups, and spectral spaces of lattice-groups
Almudena Colacito, Vincenzo Marra
Extending pioneering work by Weinberg, Conrad, McCleary, and others, we provide a systematic way of relating spaces of right orders on a partially ordered group, on the one hand, a…
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…
Tarski's Theorem on Intuitionistic logic, for polyhedra
Nick Bezhanishvili, Vincenzo Marra, Daniel McNeill +1
In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact…
Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)
Vincenzo Marra, Luca Reggio
It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the cat…
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…
From Freudenthal's Spectral Theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
Richard N. Ball, Vincenzo Marra, Daniel McNeill +1
We use a landmark result in the theory of Riesz spaces - Freudenthal's 1936 Spectral Theorem - to canonically represent any Archimedean lattice-ordered group with a strong unit…
An Analysis of Ruspini Partitions in Gödel Logic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
By a Ruspini partition we mean a finite family of fuzzy sets , , such that for all , where …
Valuations in Gödel Logic, and the Euler Characteristic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
Using the lattice-theoretic version of the Euler characteristic introduced by V. Klee and G.-C. Rota in the Sixties, we define the Euler characteristic of a formula in Gödel logic…
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…
De Vries powers: a generalization of Boolean powers for compact Hausdorff spaces
Guram Bezhanishvili, Vincenzo Marra, Patrick J. Morandi +1
We generalize the Boolean power construction to the setting of compact Hausdorff spaces. This is done by replacing Boolean algebras with de Vries algebras (complete Boolean algebra…
Two principles in many-valued logic
Stefano Aguzzoli, Vincenzo Marra
Classically, two propositions are logically equivalent precisely when they are true under the same logical valuations. Also, two logical valuations are distinct if, and only if, th…
Unital hyperarchimedean vector lattices
Richard N. Ball, Vincenzo Marra
We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that,…
The problem of artificial precision in theories of vagueness: a note on the role of maximal consistency
Vincenzo Marra
The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficie…
The Chinese Remainder Theorem for strongly semisimple MV-algebras and lattice-groups
Vincenzo Marra
An MV-algebra (equivalently, a lattice-ordered Abelian group with a distinguished order unit) is strongly semisimple if all of its quotients modulo finitely generated congruences a…
MV-algebras freely generated by finite Kleene algebras
Stefano Aguzzoli, Leonardo M. Cabrer, Vincenzo Marra
If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on h…
Idempotent generated algebras and Boolean powers of commutative rings
Guram Bezhanishvili, Vincenzo Marra, Patrick J. Morandi +1
A Boolean power S of a commutative ring R has the structure of a commutative R-algebra, and with respect to this structure, each element of S can be written uniquely as an R-linear…
Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
Mai Gehrke, Samuel J. van Gool, Vincenzo Marra
We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an esse…
The logical content of triangular bases of fuzzy sets in Łukasiewicz infinite-valued logic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Łukasiewicz logic is able to exp…