In constructive mathematics, a subset of a set is called decidable if it is classified by a function from to the Boolean domain of classical truth values. Of course, in classical mathematics, is the set of all truth values, so there every subset is decidable. (A decidable subset is alternatively called a detachable subset, at least in Fred Richman’s school.)
Equivalently, is a decidable subset of if every element of either does or does not belong to .
Working with decidable subsets of sets with decidable equality makes constructive mathematics very much like classical mathematics. This is why constructivism has few consequences for basic combinatorics and algebra (although it does have important consequences for more advanced topics in those fields). In analysis, in contrast, constructivism matters right away, because the set of real numbers may have very few decidable subsets.