Sh:506

• Shelah, S. (1997). The pcf theorem revisited. In The mathematics of Paul Erdős, II, Vol. 14, Springer, Berlin, pp. 420–459. arXiv: math/9502233 DOI: 10.1007/978-3-642-60406-5_36 MR: 1425231
• Abstract:
  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
• Version 2008-02-10_10 (63p) published version (40p)

@incollection{Sh:506,
 author = {Shelah, Saharon},
 title = {{The pcf theorem revisited}},
 booktitle = {{The mathematics of Paul Erd\H{o}s, II}},
 series = {Algorithms Combin.},
 volume = {14},
 year = {1997},
 pages = {420--459},
 publisher = {Springer, Berlin},
 mrnumber = {1425231},
 mrclass = {03E10 (04-02 04A10)},
 doi = {10.1007/978-3-642-60406-5_36},
 note = {\href{https://arxiv.org/abs/math/9502233}{arXiv: math/9502233}},
 arxiv_number = {math/9502233}
}