Constructible sets in lattice-valued models

We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B , and prove that the they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe), respectively. Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general- ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove a translation of formulas between it and a suited Heyting valued model. We also propose a notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects of it.

• Autores: Moncayo Vega, Jose Ricardo
• Fecha de publicación: 2023
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: eng
• OAI Identifier: oai:repositorio.unal.edu.co:unal/83833
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/83833; https://repositorio.unal.edu.co/
• Palabra clave: 510 - Matemáticas; Teoría de conjuntos; Set theory; Funciones de conjuntos; Set Functions; Algebra abstracta; Algebra, abstract; Valued models; Abstract logics; Residuated lattices; Kripke models; Constructible sets; Modelos valuados; Lógicas abstractas; Retículos residuales; Modelos de Kripke; Conjuntos construibles
• Rights: openAccess
• License: Atribución-NoComercial-SinDerivadas 4.0 Internacional