# 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 - published version (40p)

Bib entry

@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} }