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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

Induction Hypothesis Initial Segment Terminal Segment Ordinal Multiplication Transfinite Induction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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