Advertisement

Ordinal Arithmetic

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

Abstract

In Section 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 ∈-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 Single Element Initial Segment Prove Theorem Ordinal Number 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.University of IllinoisUSA

Personalised recommendations