Variations on a theme by Ishihara

摘要

Ishihara’s tricks have proven to be a highly useful tool in constructive mathematics, sincernthey enable one to make decisions that seem, on first glance, impossible. They do, however,rnrequire that one deals with strongly extensional mappings on complete spaces. In this shortrnnote, we show how these assumptions can be weakened. Furthermore, we apply theserngeneralizations to give a partial answer to the question, whether constructively we can rulernout the existence of injections from Baire space into the natural numbers, to a version ofrnRiemann’s per mutation theorem and to a classification problem about cardinalities inrnconstructive reverse mathematics.