Open AccessAlgebra-valued models for LP-set theory
Author(s) -
Santiago Jockwich Martinez
Publication year - 2021
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v18i7.6881
Subject(s) - interpretation (philosophy) , algebra over a field , set (abstract data type) , mathematics , model theory , point (geometry) , set theory , discrete mathematics , pure mathematics , computer science , programming language , geometry
In this paper, we explore the possibility of constructing algebra-valued models of set theory based on Priest's Logic of Paradox. We show that we can build a non-classical model of ZFC which has as internal logic Priest's Logic of Paradox and validates Leibniz's law of indiscernibility of identicals. This is achieved by modifying the interpretation map for $\in$ and $=$ in our algebra-valued model. We end by comparing our model constructions to Priest's model-theoretic strategy and point out that we have a tradeoff between desirable model-theoretic properties and the validity of ZFC and its theorems.