[**Updated December 3.** The previous proof that there is a canonical bijection for all infinite ordinals was seriously flawed. Thanks to Lorenzo Traldi for pointing out the problem.]

5. Specker’s lemma.

This result comes from Ernst Specker, *Verallgemeinerte Kontinuumshypothese und Auswahlaxiom*, Archiv der Mathematik **5 **(1954), 332-337. I follow Akihiro Kanamori, David Pincus, *Does GCH imply AC locally?, *in **Paul Erdős and his mathematics, II (Budapest, 1999)**, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, (2002), 413-426 in the presentation of this and the following result. The Kanamori-Pincus paper, to which we will return next lecture, has several interesting problems, results, and historical remarks, and I recommend it. It can be found here.