10 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…
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…
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 Åukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Åukasiewic…
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…