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Relational Closure and the Rank Function

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

Abstract

In this chapter we introduce two ideas important for the work to follow. The first of these is relational closure. In later chapters we will be especially interested in sets that are transitive. While there exist sets that are not transitive every set has a transitive extension. Indeed, every set has a smallest transitive extension which we call its transitive closure.

Keywords

Relational Closure Induction Hypothesis Rank Function Transitive Closure Minimal Rank 
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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