In this paper we shall discuss some classes of general monotonic neighbourhood frames, or general... more In this paper we shall discuss some classes of general monotonic neighbourhood frames, or general m-frames. We shall study the classes of point-compact, image compact and replete general m-frames, and the relationships between them. The variety of Boolean algebras with a monotonic modal operator is dually equivalent to two classes of descriptive general m-frames. In this paper we shall clarify this phenomenon showing that there exists a bijective correspondence between these two classes. We shall also prove that the notions of point-compact, and image-compact monotonic frames are preserved by strong bounded morphisms. Also, we will prove some preservation results on general subframes.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Menchón, María Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentin
In this note we will investigate some particular classes of ideals in Hilbert algebras with supre... more In this note we will investigate some particular classes of ideals in Hilbert algebras with supremum. We shall study the relation between -ideals and annihilator ideals in bounded Hilbert algebras with supremum. We shall introduce the class of -ideals and we will see that this class is strongly connected with the deductive systems. We will also characterize the bounded Hilbert algebras with supremum satisfying the Stone identity.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic s... more In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic semantics of the order implicational calculus of Bull (J Symb Logic, 29:33–34, 1964).
In recent years Esakia duality for Heyting algebras has been extended in two directions. First to... more In recent years Esakia duality for Heyting algebras has been extended in two directions. First to weak Heyting algebras, namely distributive lattices with an implication with weaker properties than that of the implication of a Heyting algebra, and secondly to implicative semilattices. The first algebras correspond to subintuitionistic logics, the second ones to the conjunction and implication fragment of intuitionistic logic. Esakia duality has also been complemented with dualities for categories whose objects are Heyting algebras and whose morphisms are maps that preserve less structure than homomorphisms of Heyting algebras. In this chapter we survey these developments.
A subresiduated lattice is a pair , where A is a bounded distributive lattice, D is a bounded sub... more A subresiduated lattice is a pair , where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set , which is denoted by . This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where . The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by , whose members satisfy the equation . Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every .
In this paper we shall discuss some classes of general monotonic neighbourhood frames, or general... more In this paper we shall discuss some classes of general monotonic neighbourhood frames, or general m-frames. We shall study the classes of point-compact, image compact and replete general m-frames, and the relationships between them. The variety of Boolean algebras with a monotonic modal operator is dually equivalent to two classes of descriptive general m-frames. In this paper we shall clarify this phenomenon showing that there exists a bijective correspondence between these two classes. We shall also prove that the notions of point-compact, and image-compact monotonic frames are preserved by strong bounded morphisms. Also, we will prove some preservation results on general subframes.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Menchón, María Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentin
In this note we will investigate some particular classes of ideals in Hilbert algebras with supre... more In this note we will investigate some particular classes of ideals in Hilbert algebras with supremum. We shall study the relation between -ideals and annihilator ideals in bounded Hilbert algebras with supremum. We shall introduce the class of -ideals and we will see that this class is strongly connected with the deductive systems. We will also characterize the bounded Hilbert algebras with supremum satisfying the Stone identity.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic s... more In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic semantics of the order implicational calculus of Bull (J Symb Logic, 29:33–34, 1964).
In recent years Esakia duality for Heyting algebras has been extended in two directions. First to... more In recent years Esakia duality for Heyting algebras has been extended in two directions. First to weak Heyting algebras, namely distributive lattices with an implication with weaker properties than that of the implication of a Heyting algebra, and secondly to implicative semilattices. The first algebras correspond to subintuitionistic logics, the second ones to the conjunction and implication fragment of intuitionistic logic. Esakia duality has also been complemented with dualities for categories whose objects are Heyting algebras and whose morphisms are maps that preserve less structure than homomorphisms of Heyting algebras. In this chapter we survey these developments.
A subresiduated lattice is a pair , where A is a bounded distributive lattice, D is a bounded sub... more A subresiduated lattice is a pair , where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set , which is denoted by . This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where . The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by , whose members satisfy the equation . Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every .
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