1998 | OriginalPaper | Buchkapitel
Cardinal and Ordinal Numbers
verfasst von : S. M. Srivastava
Erschienen in: A Course on Borel Sets
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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In this chapter we present some basic set-theoretical notions. The first five sectionsl 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.