Abstract:The uncountability of R is one of its most basic properties, known far outside of mathematics. Cantor's 1874 proof of the uncountability of R even appears in the very first paper on set theory, i.e. a historical milestone. In this paper, we study the uncountability of R in Kohlenbach's higher-order Reverse Mathematics (RM for short), in the guise of the following principle:An important conceptual observation is that the usual definition of countable set -based on injections or bijections to N-does not seem sui… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.