For more information about countable and uncountable sets, see books about "Analysis" (as advanced calculus is called). For example, Introductory Real Analysis, by A.N. Kolmogorov and S.V. Fomin (see ...

Proceedings of the American Mathematical Society, Vol. 111, No. 3 (Mar., 1991), pp. 841-844 (4 pages) We make the translations of our partitions from [3] in the context of all countable subsets of a ...

Let μ be singular of uncountable cofinality. If μ > 2cf(μ), we prove that in P = ([μ]μ, ⊇) as a forcing notion we have a natural complete embedding of Levy (‮א‬₀, μ⁺) (so P collapses μ⁺ to ‮א‬₀) and ...