Applications of PCF theory

Journal of Symbolic Logic 65 (4):1624-1674 (2000)

We deal with several pcf problems: we characterize another version of exponentiation: maximal number of κ-branches in a tree with λ nodes, deal with existence of independent sets in stable theories, possible cardinalities of ultraproducts and the depth of ultraproducts of Boolean Algebras. Also we give cardinal invariants for each λ with a pcf restriction and investigate further T D (f). The sections can be read independently, although there are some minor dependencies
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DOI 10.2307/2695067
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References found in this work BETA

Reflecting Stationary Sets and Successors of Singular Cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Cardinal Invariants Above the Continuum.James Cummings & Saharon Shelah - 1995 - Annals of Pure and Applied Logic 75 (3):251-268.
Set Theory Without Choice: Not Everything on Cofinality is Possible.Saharon Shelah - 1997 - Archive for Mathematical Logic 36 (2):81-125.
On Power of Singular Cardinals.Saharon Shelah - 1986 - Notre Dame Journal of Formal Logic 27 (2):263-299.

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Citations of this work BETA

On Long Increasing Chains Modulo Flat Ideals.Saharon Shelah - 2010 - Mathematical Logic Quarterly 56 (4):397-399.
Middle Diamond.Saharon Shelah - 2005 - Archive for Mathematical Logic 44 (5):527-560.
More on the Revised GCH and the Black Box.Saharon Shelah - 2006 - Annals of Pure and Applied Logic 140 (1):133-160.
More on Regular and Decomposable Ultrafilters in ZFC.Paolo Lipparini - 2010 - Mathematical Logic Quarterly 56 (4):340-374.

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