 First, we define a set \(S\) to be countable if there is a mapping from a detachable subset of \(\bN\) onto \(S\). With intuitionistic logic we cannot prove that every subset of \(\bN\) is detachable (the reader is invited to provide a Brouwerian example to demonstrate this). Countable subsets of \(\bN\) in Richman’s axiomatic approach are the counterparts of recursively enumerable sets in the normal development of RUSS.