Cardinal and Ordinal Numbers

Abstract p]In this chapter we present some basic set-theoretical notions. The first five sections¹ are devoted to cardinal numbers. We use Zorn’s lemma to develop cardinal arithmetic. Ordinal numbers and the methods of transfinite induction on well-ordered sets are presented in the next four sections. Finally, we introduce trees and the Souslin operation. Trees are also used in several other branches of mathematics such as infinitary combinatorics, logic, computer science, and topology. The Souslin operation is of special importance to descriptive set theory, and perhaps it will be new to some readers.

These are produced here from my article [117] with the permission of the Indian Academy of Sciences.