Overview
Super-real fields are a class of large totally ordered fields. These fields are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are of interest in their own right and have many surprising applications, both in analysis and logic. The authors introduce some exciting new fields, including a natural generalization of the real line R, and resolve a number of open problems. The book is intended to be accessible to analysts and logicians. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kaplansky's embedding theorems , the authors establish important new results in Banach algebra theory, non-standard analysis, an model theory.
Full Product Details
Author: H. Garth Dales (Proessor of Pure Mathematics, Proessor of Pure Mathematics, University of Leeds) ,
W. Hugh Woodin (Professor of Mathematics, Professor of Mathematics, University of California, Berkeley, USA)
Publisher: Oxford University Press
Imprint: Oxford University Press
Volume: 14
Dimensions:
Width: 16.20cm
, Height: 2.20cm
, Length: 24.10cm
Weight: 0.682kg
ISBN: 9780198539919
ISBN 10: 0198539916
Pages: 376
Publication Date: 16 May 1996
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: To order
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.
Reviews
This book is an interesting research monograph which, because of its several fine introductory chapters, should be accessible to a large number of readers ... The breadth and depth of the analysis and synthesis of the additional structure , used to prove some of these theorems, is impressive . * Zentrallblat fur Mathematik, vol. 856, 1997 *
"`This book is an interesting research monograph which, because of its several fine introductory chapters, should be accessible to a large number of readers ... The breadth and depth of the analysis and synthesis of the ""additional structure"", used to prove some of these theorems, is impressive .' Zentrallblat fur Mathematik, vol. 856, 1997"
This book is an interesting research monograph which, because of its several fine introductory chapters, should be accessible to a large number of readers ... The breadth and depth of the analysis and synthesis of the additional structure , used to prove some of these theorems, is impressive . Zentrallblat fur Mathematik, vol. 856, 1997
