 A set which satisfies \(|A| = |\wp_1 (A)|\) is called a cantorian set, since it satisfies the usual form of Cantor’s theorem. A set \(A\) which satisfies the stronger condition that the restriction of the singleton map to \(A\) is a set is said to be strongly cantorian (s.c.). Strongly cantorian sets are important because it is not necessary to assign a relative type to a variable known to be restricted to a strongly cantorian set, as it is possible to use the restriction of the singleton map and its inverse to freely adjust the type of any such variable for purposes of stratification. The strongly cantorian sets are can be thought of as analogues of the small sets of the usual set theory.