### The pcf-theorem revisited

by Shelah. [Sh:506]

Math Paul Erd\H{o}s, II, 1997

The textrm {pcf} theorem (of the possible cofinality theory)
was proved for reduced products prod_{i< kappa} lambda_i/I, where
kappa < min_{i< kappa} lambda_i . Here we prove this
theorem under weaker assumptions such as wsat(I)<
min_{i< kappa} lambda_i, where wsat(I) is the minimal
theta such that kappa cannot be delivered to theta sets
notin 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(lambda) . Finally we apply this to the problem
of the depth of ultraproducts (and reduced products) of Boolean
algebras

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