The PCF Theorem Revisited

  • Saharon Shelah
Part of the Algorithms and Combinatorics book series (AC, volume 14)


The pcf theorem (of the possible cofinability theory) was proved for reduced products \(\prod\limits_{i < k} {{\lambda _i}/I}\), where κ < min i<κ λ i . Here we prove this theorem under weaker assumptions such as wsat(I) < min i<κ λ i , where wsat(I) is the minimal θ such that κ cannot be divided to θ sets ∉ I (or even slightly weaker condition). We also look at the existence of exact upper bounds relative to < I (< I —eub) as well as cardinalities of reduced products and the cardinals T D (λ). Finally we apply this to the problem of the depth of ultraproducts (and reduced products) of Boolean algebras.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Saharon Shelah
    • 1
    • 2
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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