Tropicalization through the lens of Łukasiewicz logic, with a topos theoretic perspective

The main aim of this paper is to show the interconnections between Łukasiewicz logic and algebraic geometry using algebraic, geometric and logical instruments. We continue our investigation into a new algebraic geometry based on idempotent semifields, in particular those related with MV-algebras, describing categorical equivalence between different structures related to tropical geometry and many valued logics. Further, we describe such connections in terms of topoi.