The PCF theorem revisited

Saharan Shelah*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

The pcf theorem (of the possible cofinability theory) was proved for reduced products ∏i<κλi/I, where κ<mini<κλi. Here we prove this theorem under weaker assumptions such as wsat(I)<mini<κλi, where wsat(I) is the minimalθsuch thatκcannot be divided toθsets ∉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 cardinalsT D (λ).Finally we apply this to the problem of the depth of ultraproducts (and reduced products) of Boolean algebras.

Original languageEnglish
Title of host publicationThe Mathematics of Paul Erdos II, Second Edition
PublisherSpringer New York
Pages441-488
Number of pages48
ISBN (Electronic)9781461472544
ISBN (Print)9781461472537
DOIs
StatePublished - 1 Jan 2013

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2013.

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