Hannes Diener: Completeness is overrated

Abstract: It is a common theme in constructive mathematics that adding completeness to the assumptions often allows us to prove otherwise constructively unprovable statements. In this talk we show that we actually only need a very weak version of completeness. We also show that there is an enormous amount of spaces that aren’t complete, but satisfy the weakened version of completeness, thus generalising many theorems of constructive analysis.