English

Tropicalization through the lens of {\L}ukasiewicz logic, with a topos theoretic perspective

Logic 2025-01-14 v2

Abstract

The main aim of this paper is to show the interconnections between {\L}ukasiewicz 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.

Keywords

Cite

@article{arxiv.2409.08682,
  title  = {Tropicalization through the lens of {\L}ukasiewicz logic, with a topos theoretic perspective},
  author = {Antonio Di Nola and Giacomo Lenzi and Brunella Gerla},
  journal= {arXiv preprint arXiv:2409.08682},
  year   = {2025}
}