
Super-Real Fields
Totally Ordered Fields with Additional Structure
Oxford University Press
Published on 16. May 1996
Book
Hardback
376 pages
978-0-19-853991-9 (ISBN)
Description
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 / Votes
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 *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Illustrations
line figures
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 25 mm
Weight
728 gr
ISBN-13
978-0-19-853991-9 (9780198539919)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Author
Proessor of Pure MathematicsProessor of Pure Mathematics, University of Leeds
Professor of MathematicsProfessor of Mathematics, University of California, Berkeley, USA
Content
Introduction ; 1. Ordered sets and ordered groups ; 2. Ordered fields ; 3. Completions of ordered groups and fields ; 4. Algebras of continuous functions ; 5. Normability and universality ; 6. The operational calculus and the field R ; 7. Examples ; 8. Non-standard structures for super-real fields and the gap theorem ; 9. R as a hyper-real field ; 10. Models and weak Cauchy completeness ; 11. Rigid fields and solids structures ; 12. Open questions