Linear models and set theory

Abstract

In this paper we review the approach to algebra-valued models and we introduce an in nite class of natural models for paraconsistent set theory. We then present several paraconsistent set theories based on Logics of Formal Inconsistency (LFI), known in the literature as LFI-set theories, and we show that there is no natural model that validates these systems. We therefore suggest to abandon these theories.