LOGICAL BERKOVICH GEOMETRY: A POINT-FREE PERSPECTIVE
Abstract
Extending our insights from \cite{NVOstrowski}, we apply point-free techniques to sharpen a foundational result in Berkovich geometry. In our language, given the ring $\mathcal{A}:=K\{R^{-1}T\}$ of convergent power series over a suitable non-Archimedean field $K$, the points of its Berkovich Spectrum $\mathcal{M}(\mathcal{A})$ correspond to $R$-good filters. The surprise is that, unlike the original result by Berkovich, we do not require the field $K$ to be non-trivially valued. Our investigations into non-Archimedean geometry can be understood as being framed by the question: what is the relationship between topology and logic?
Fields of Study & Subjects
Mathematical and Theoretical Analysis
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Journal of Symbolic Logic
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–33
- Publication date
- 15 June 2026
- Language
- EN