arXiv subjects

Sergio A. Celani

Publications and source records attributed to Sergio A. Celani.

4 recordsLinked to original sources

arXiv2026

A bitopological duality for some subordination Boolean algebras

S4-subordination algebras are a generalization of the closure algebras. In this paper, we give a topological representation for S4-subordination algebras by means of bitopological spaces $\left $, where $\left $ is a Stone space and $τ_{S}$ is a topology that enables the characterization of the subordination relation. We apply this bitopological representation to give a characterization of S5-subordination algebras and lattice subordinations. We also show that there exists a bijective correspondence between congruence compatible with the subordination and certain closed subsets of the Stone space $\left $ that are also saturated sets of the space $\left $. Additionally, we explore two types of morphisms between S4-subordination algebras: one based on Boolean homomorphisms and another based on meet-homomorphisms. Finally, we provide a topological representation for each type of morphism.

math.LO↗

arXiv2026

Priestley Representation of Distributive Precontact Lattices

It is well known that, in Boolean algebras, the notions of precontact relation, quasi-modal operator, and subordination relation are interdefinable. In contrast, within the setting of distributive lattices, this equivalence holds only between quasi-modal operators and subordination relations, but not with precontact relations. In this paper, we study the class of bounded distributive lattices equipped with a precontact relation, referred to as precontact lattices. We also examine how conditions imposed on the precontact relation correspond to first-order properties in the Priestley dual. In addition, we characterize precontact substructures and strong precontact sublattices of precontact lattices in terms of a suitable lattice preorder. Finally, we introduce a notion of precontact congruence and identify the corresponding closed sets in the dual space.

math.LO↗

arXiv2018

Monotonic Distributive Semilattices

In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the $\{\rightarrow,\wedge,\top\}$-fragment of intuitionistic logic is the variety of implicative meet-semilattices \cite{CelaniImplicative} \cite{ChajdaHalasKuhr}. In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator $m$. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.

math.LO↗

arXiv2018

Prelinear Hilbert algebras

In this paper we give an explicit description of the left adjoint of the forgetful functor from the algebraic category of Gödel algebras (i.e., prelinear Heyting algebras) to the algebraic category of bounded prelinear Hilbert algebras. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras.

math.LO↗