Ordinal Arithmetic

  • Gaisi Takeuti
  • Wilson M. Zaring
Part of the Graduate Texts in Mathematics book series (GTM, volume 1)

Abstract

In Chapter 7 we defined α + 1 to be α ∪ {α}. We proved that α + 1 is an ordinal, that is, α + 1 is a transitive set that is well ordered by the e-relation. As a well-ordered set α + 1 has an initial segment α and its “terminal” segment beginning with α consists of just a single element, namely α.

Keywords

Assure 

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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