 On the other hand, in Bishop-style mathematics, completely presented–––or, in his terminology, basic–––sets are rare, one example being \(\bN\); so we might expect that the axiom of choice would not be derivable. In fact, as was shown by Diaconescu [1975] and Goodman &amp; Myhill [1978], and prefigured by Bishop himself in Problem 2 on page 58 of Bishop 1967, the axiom of choice implies the law of excluded middle. Clearly, the Diaconescu-Goodman-Myhill theorem applies only under the assumption that not every set is completely presented.