Intuitionism and Computer Science – Why Computer Scientists do not Like the Axiom of Choice
Thomas Fehlmann, Eberhard Kranich · Athens Journal of Sciences · 2020
The Axiom of Choice (AC) says that every set has a representative element.However, deterministic computers cannot produce arbitrary elements.They need some algorithm that tells them, which one to choose.But then, the element is no longer arbitrary.Even for a true random generator, you will need entropy.This is data gathered from outside the system, and we as Theoretical Computer scientists do not like that.Thus, we need to understand the Axiom of Choice better.For this, we use a model of Combinatory Logic.