Cardinal Arithmetic
Book Details
Format
Hardback or Cased Book
Book Series
Oxford Logic Guides
ISBN-10
0198537859
ISBN-13
9780198537854
Publisher
Oxford University Press
Imprint
Clarendon Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Nov 17th, 1994
Print length
512 Pages
Weight
783 grams
Dimensions
24.20 x 16.00 x 3.20 cms
Product Classification:
Mathematical logicSet theory
Ksh 52,200.00
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Setting a new direction in research in the subject, this book presents a new view of cardinal arithmetic, one of the central issues in set theory. Focusing on cofinalities rather than cardinalities, new results are obtained and published here for the first time.
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 Gödel and Cohen (and Easton) with some isolated positive results (like Galvin-Hajnal). It was expected that only more independence results remained to be proved.The author has come to change his view: we should stress Π]*N0 (not 2]Π) and mainly look at the cofinalities rather than cardinalities, in particular pp (μ), pcf (α). Their properties are investigated here and conventional cardinal arithmetic is reduced to 2]*N (*N - regular, cases totally independent) and various cofinalities. 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.
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