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Extending our insights from \cite{NVOstrowski}, we apply point-freetechniques to sharpen a foundational result in Berkovich geometry. In ourlanguage, given the ring $\mathcal{A}:=K\{R^{-1}T\}$ of convergent power seriesover a suitable non-Archimedean field $K$, the points of its Berkovich Spectrum$\mathcal{M}(\mathcal{A})$ correspond to $R$-good filters. The surprise isthat, unlike the original result by Berkovich, we do not require the field $K$to be non-trivially valued. Our investigations into non-Archimedean geometrycan be understood as being framed by the question: what is the relationshipbetween topology and logic?

Logical Berkovich Geometry: A Point-free Perspective