4 papers · 1 filter
Avoiding logical strength in real analysis
Anton Freund, Nicholas Pischke, Patrick Uftring
In reverse mathematics, real numbers are traditionally represented by Cauchy sequences with a given rate of convergence. We work without rates and speak of slow Cauchy sequences. I…
A systematic way of analysing proofs in probability theory
Morenikeji Neri, Paulo Oliva, Nicholas Pischke
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of pr…
A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications
Nicholas Pischke
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-com…
Proof mining and probability theory
Morenikeji Neri, Nicholas Pischke
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima f…