Cardinal Arithmetic by Saharon ShelahCardinal Arithmetic by Saharon Shelah

Cardinal Arithmetic

bySaharon Shelah

Hardcover | March 1, 1988

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Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence results of Godel and Cohen (and Easton) with some isolated positive results (likeGalvin-Hajnal). It was expected that only more independence results remained to be proved. The author has come to change his view. This enables us to get new results for the conventional cardinal arithmetic, thus supporting the interest in our view. We also find other applications, extend older methods of using normal fiters and prove the existence of Jonsson algebra.
Saharon Shelah is at The Hebrew University of Jerusalem.
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Title:Cardinal ArithmeticFormat:HardcoverDimensions:512 pages, 9.21 × 6.14 × 1.26 inPublished:March 1, 1988Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198537859

ISBN - 13:9780198537854

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Table of Contents

1. Basic confinalities of small reduced products2. No+1 has a Jonsson algebra3. There are Jonsson algebras in many inaccessible cardinals4. Jonsson algebras in inaccessibles P , not P-Mahlo5. Bounding pp(m ) when m cf(m) N0 using ranks and normal filters6. Bounds of power of singulars: Induction7. Strong covering lemma and CH in V[r]8. Advanced: Cofinalities of reduced products9. Cardinal ArithmeticAppendix 1: ColoringsAppendix 2: Entangled orders and narrow Boolean algebras

Editorial Reviews

This is a very important book. It is essential reading for anyone working in set theory and its applications. Bull.London Math.Soc.