Constructive reverse mathematics : Habilitationsschrift

We give a comprehensive treatment of the area known as constructive reverse mathematics, which aims to classify, over intuitionistic logic, various theorems in intuitionistic, constructive recursive, and classical mathematics. Our work provides an overview of many known results, but also many new results, and new proofs of known results. We cover omniscience principles, Markov’s principle, Brouwer’s fan theorem(s), recursive principles, Ishihara’s boundedness principle BD-N, as well as minor principles, and separation techniques.