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arXiv · 2409.08682

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

Antonio Di Nola·Giacomo Lenzi·Brunella Gerla
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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.

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Antonio Di Nola, Giacomo Lenzi, Brunella Gerla. 2024-09-13. Tropicalization through the lens of {\L}ukasiewicz logic, with a topos theoretic perspective. https://arxiv.org/abs/2409.08682

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