Cardinal Arithmetic and the Cantor Set

Abstract

We continue the basic theory of cardinals, covering the Cantor–Bernstein Theorem, arbitrary cardinal products and cardinal arithmetic, binary trees and the construction of the Cantor set, the identity \({2}^{\aleph _{0}} =\boldsymbol{ \mathfrak{c}}\) and effective bijections between familiar sets of cardinality \(\boldsymbol{\mathfrak{c}}\), Cantor’s theorem and Konig’s inequality, and the behavior of \({\kappa }^{\aleph _{0}}\) for various cardinals κ.