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 language | English |
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Title of host publication | The Mathematics of Paul Erdos II, Second Edition |
Publisher | Springer New York |
Pages | 441-488 |
Number of pages | 48 |
ISBN (Electronic) | 9781461472544 |
ISBN (Print) | 9781461472537 |
DOIs | |
State | Published - 1 Jan 2013 |
Bibliographical note
Publisher Copyright:© Springer Science+Business Media New York 2013.