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.
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 *



Book Information
ISBN 9780198539919
Author H. Garth Dales
Format Hardback
Page Count 376
Imprint Oxford University Press
Publisher Oxford University Press
Weight(grams) 682g
Dimensions(mm) 241mm * 162mm * 22mm