3 papers
math.AG2023
Logical Berkovich Geometry: A Point-free Perspective
Ming Ng
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}:…
math.NT2023
A Point-Free Look at Ostrowski's Theorem and Absolute Values
Ming Ng, Steven Vickers
This paper investigates the absolute values on valued in the upper reals (i.e. reals for which only a right Dedekind section is given). These necessarily include multi…
math.CT2021
Point-free Construction of Real Exponentiation
Ming Ng, Steven Vickers
We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, ζ) \…