The Cantor theorem of the usual set theory asserts that \(|A| \lt |\wp(A)|\). This is clearly not true in NFU, since | \(V|\) is the cardinality of the universe and \(|\wp(V)|\) is the cardinality of the set of sets, and in fact \(|V| \gt \gt |\wp(V)|\) in all known models of NFU (there are many intervening cardinals in all such models). But \(|A| \lt |\wp(A)|\) does not make sense in TST: it is ill-typed. The correct theorem in TST, which is inherited by NFU, is \(|\wp_1 (A)| \lt |\wp(A)|\), wh