Kripke-like models of Set Theory in Modal Residuated Logic
arxiv(2024)
Abstract
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 generalization 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 constructible
sets in Modal Residuated Logic and discuss some aspects of it.
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