1 Statement of results Write |M| for the cardinal number of a set M and let P(M) denote the power set of M , P(M) = {X | X ⊂ M}. If |M| = κ then |P(M)| = 2 . In particular, c = 2א0 where as usual א0 = |N| and c = |R|. For any transfinite cardinal κ let κ+ denote the least cardinal number greater than κ . (For example, א0 = א1, א1 = א2, . . .) Naturally, κ < κ+ ≤ 2 . Neither κ+ = 2 nor κ+ < 2 is...