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The Axiom of Choice, the Generalized Continuum Hypothesis and Cardinal Arithmetic

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

Abstract

In Section 10 we defined the cardinal number of a set,
$$ \overline{\overline a} $$
, to be the smallest ordinal that is equivalent to a. If no such ordinal exists then
$$ \overline{\overline a} = 0 $$
. This definition has the advantage of connecting the theory of cardinal numbers to the properties of ordinals. A more traditional view is that
$$ \overline{\overline a} $$
is the equivalence class of sets equipollant to a.

Keywords

Equivalence Class Maximal Element Choice Function Strong Form Cardinal 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

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

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