Kripke-like models of Set Theory in Modal Residuated Logic

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.