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arXiv · 2405.04641

Kripke-like models of Set Theory in Modal Residuated Logic

Jose Moncayo·Pedro H. Zambrano
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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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Jose Moncayo, Pedro H. Zambrano. 2024-05-07. Kripke-like models of Set Theory in Modal Residuated Logic. https://arxiv.org/abs/2405.04641

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