The PCF Theorem Revisited

  title={The PCF Theorem Revisited},
  author={Saharan Shelah},
  booktitle={The Mathematics of Paul Erdős II},
i<κ λi/I, where κ < mini<κ λi. Here we prove this theorem under weaker assumptions such as wsat(I) < mini<κ λi, where wsat(I) is the minimal θ such that κ cannot be delivered 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 TD(λ). Finally we apply this to the problem of the depth of ultraproducts (and reduced products) of Boolean algebras. 

From This Paper

Topics from this paper.


Publications citing this paper.
Showing 1-2 of 2 extracted citations


Publications referenced by this paper.
Showing 1-10 of 10 references

Cardinal Artihmetic, volume 29 of Oxford Logic Guides, General Editors

  • S. Shelah
  • 1994

Cardinal Function on Boolean Algebras, Lectures in Mathmatics, ETH Zürich, Bikhäuser

  • J. D. Monk
  • 1990

Products of regular cardinals and cardinal invariants of Boolean Algebra, Israel

  • S. Shelah
  • Journal of Mathematics,
  • 1990

Some combinatorial properties of ultra-filters

  • J. Ketonen
  • Fund Math. VII
  • 1980

Similar Papers

Loading similar papers…