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A Partition Calculus in Set Theory

  • P. Erdös
  • R. Rado
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Dedekind’s pigeon-hole principle, also known as the box argument or the chest of drawers argument (Schubfachprinzip) can be described, rather vaguely, as follows. If sufficiently many objects are distributed over not too many classes, then at least one class contains many of these objects. In 1930 F. P. Ramsey [12] discovered a remarkable extension of this principle which, in its simplest form, can be stated as follows. Let S be the set of all positive integers and suppose that all unordered pairs of distinct elements of S are distributed over two classes.

Keywords

Equivalence Relation Order Type Unordered Pair Partition Relation Require Contradiction 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • P. Erdös
    • 1
  • R. Rado
    • 2
  1. 1.Hebrew University of JerusalemJerusalemIsrael
  2. 2.University of RudingJerusalemIsrael

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