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math.CT2023
The Fundamental Theorem of Calculus point-free, with applications to exponentials and logarithms
Steven Vickers
Working in point-free topology under the constraints of geometric logic, we prove the Fundamental Theorem of Calculus, and apply it to prove the usual rules for the derivatives of…
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…