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

Abstract

We pointed out in the introduction that one objective of axiomatic set theory is to avoid the classical paradoxes. One such paradox, the Russell paradox, arose from the naive acceptance of the idea that given any property there exists a set whose elements are those objects having the given property, i.e., given a wff φ (x) containing no free variables other than x, there exists a set that contains all objects for which φ (x) holds and contains no object for which φ(x) does not hold. More formally \((\exists a)(\forall x)[x \in a \leftrightarrow \varphi (x)]\).

Keywords

Individual Variable Free Variable Object Language Effective Procedure Wide Sense 
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. 2.
    van Heijenoort, Jean: From Frege to Gödel. Cambridge: Harvard University Press 1967, pp. 124–125.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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