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Equality

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

Abstract

Definition 3.1 is incomplete in that the variable x does not occur in a = b, consequently we have not made clear which of the infinitely many formulas, equivalent under alphabetic change of variable, we intend a = b to be an abbreviation for. This problem is easily resolved by specifying that x is the first variable an our list
$$ {x_0},\,{x_1}, \ldots $$
that is distinct from a and from b. Having thereby shown that we can specify a particular formula we will not bother to do so either here or in similar definitions to follow.

Keywords

Basic Property Induction Hypothesis Publishing Company Intuitive Idea Similar Definition 
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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References

  1. 1.
    Essays on the Foundations of Mathematics. Amsterdam: North-Holland Publishing Company, 1962, pp. 115–131.Google Scholar
  2. 2.
    See Quine, Van Orman: Set Theory and its Logic. Cambridge: Mass. Harvard University Press 1969, 30f.MATHGoogle Scholar

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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