Quantale-Valued Model Theory and Set Theory

Abstract: In this talk, we will discuss a generalization of Continuous Logic, where the distances take values in suitable quantales. By assuming suitable conditions (e.g., being co-divisibility -substractability-, being a co-Girard and a V-domain), we provide a proof of a version of the Tarski-Vaught test and Łoś Theorem in our setting. Iovino proved that there is no logic properly extending Continuous Logic satisfying both Countable Tarski-Vaught chain Theorem and Compactness Theorem, obtaining in this way a new approach of Continuous Logic. This part is a joint work with David Reyes. Also, we will talk about a generalization of Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono’s 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 (close to quantales) and prove a translation of formulas between it and a suited Heyting valued model. This part is a joint work with Jose R. Moncayo.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic