Sesión Lógica y ComputabilidadA categorical equivalence for tense pseudocomplemented distributive lattices
Maia Starobinsky
Instituto de Ciencias Básicas, Universidad Nacional de San Juan y Facultad de Ciencias Económicas, Universidad de Buenos Aires, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
A pseudocomplemented distributive lattice (also known as a distributive $p$-algebra) is an algebraic structure denoted as $\langle A, \wedge, \vee, \ast, 0, 1 \rangle$, where the underlying structure $\langle A, \wedge, \vee, 0, 1 \rangle$ is a bounded distributive lattice, and the unary operation $\ast$ represents a pseudocomplement operation [1]. This operation satisfies the property that $x \wedge y = 0$ if and only if $x \leq y^\ast$.
In this paper, our motivation stems from the definition of tense operators on distributive lattices proposed by Chajda and Paseka in [2]. We introduce and explore the variety of tense pseudocomplemented distributive lattices. Specifically, we establish a categorical equivalence of these structures with a full subcategory of tense KAN-algebras.
Trabajo en conjunto con: Gustavo Pelaitay (Instituto de Ciencias Básicas, Universidad Nacional de San Juan y CONICET).
Referencias
[1] Balbes, R., Dwinger P., Distributive Lattices. University of Missouri Press (1974)
[2] I.Chajda, J.Paseka: Algebraic Appropach to Tense Operators, Research and Exposition in Mathematics Vol. 35, Heldermann Verlag (Germany), 2015, ISBN 978-3-88538-235-5.