On one of Specker's theorems

摘要

? 2022 Elsevier B.V.The Specker theorem is considered, stating that if for some cardinal m there is no strictly intermediate cardinal between m and 2m (briefly CH(m)), and also between 2m and 22m (briefly CH(2m)), then the cardinal 2m is an aleph (briefly WO(2m)). Rejecting the second condition CH(2m) in Specker's theorem, a different condition of local bounded selection of elements from the family of bijections of the set X, X=m, to sets X?0,α), 0<α