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The Cardinal Function pp(λ)

  • M. Holz
  • K. Steffens
  • E. Weitz
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In this chapter, we introduce Shelah’s cardinal function pp k (λ) whose properties we now summarize. If λ is a singular cardinal, then the definition of pp k (λ) gives pp k (λ) ≤ λ k for any cardinal k with cf (λ) ≤ k < λ. For singular cardinals λ with uncountable cofinality and k = cf (λ) which are in addition k-strong, we get pp k (λ) = λ k . In particular pp k (λ) = 2λ holds for every strong limit cardinal λ with uncountable cofinality k.

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Copyright information

© Springer Basel AG 1999

Authors and Affiliations

  • M. Holz
    • 1
  • K. Steffens
    • 1
  • E. Weitz
    • 2
  1. 1.Institut für MathematikUniversität HannoverHannoverGermany
  2. 2.HamburgGermany

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