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  1.  23
    Hilbert Algebras with a Modal Operator $${\Diamond}$$ ◊.Sergio A. Celani & Daniela Montangie - 2015 - Studia Logica 103 (3):639-662.
    A Hilbert algebra with supremum is a Hilbert algebra where the associated order is a join-semilattice. This class of algebras is a variety and was studied in Celani and Montangie . In this paper we shall introduce and study the variety of $${H_{\Diamond}^{\vee}}$$ H ◊ ∨ -algebras, which are Hilbert algebras with supremum endowed with a modal operator $${\Diamond}$$ ◊ . We give a topological representation for these algebras using the topological spectral-like representation for Hilbert algebras with supremum given in (...)
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  2.  4
    Hilbert Algebras with Hilbert–Galois Connections.Sergio A. Celani & Daniela Montangie - 2023 - Studia Logica 111 (1):113-138.
    In this paper we introduce Hilbert algebras with Hilbert–Galois connections (HilGC-algebras) and we study the Hilbert–Galois connections defined in Heyting algebras, called HGC-algebras. We assign a categorical duality between the category HilGC-algebras with Hilbert homomorphisms that commutes with Hilbert–Galois connections and Hilbert spaces with certain binary relations and whose morphisms are special functional relations. We also prove a categorical duality between the category of Heyting Galois algebras with Heyting homomorphisms that commutes with Hilbert–Galois connections and the category of spectral Heyting (...)
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  3. 10. Lógica y Computabilidad.Sergio Celani, Daniela Montangie & Álgebras de Hilbert Modales - 2001 - Journal of Symbolic Logic 66:1620-1636.
     
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