Super-Real Fields
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Home > Mathematics and Science Textbooks > Mathematics > Algebra > Super-Real Fields: Totally Ordered Fields with Additional Structure(14 London Mathematical Society Monographs)
Super-Real Fields: Totally Ordered Fields with Additional Structure(14 London Mathematical Society Monographs)

Super-Real Fields: Totally Ordered Fields with Additional Structure(14 London Mathematical Society Monographs)


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About the Book

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.

Table of Contents:
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

Review :
`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


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Product Details
  • ISBN-13: 9780198539919
  • Publisher: Oxford University Press
  • Publisher Imprint: Oxford University Press
  • Height: 241 mm
  • No of Pages: 376
  • Series Title: 14 London Mathematical Society Monographs
  • Sub Title: Totally Ordered Fields with Additional Structure
  • Width: 162 mm
  • ISBN-10: 0198539916
  • Publisher Date: 16 May 1996
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Spine Width: 22 mm
  • Weight: 682 gr


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Super-Real Fields: Totally Ordered Fields with Additional Structure(14 London Mathematical Society Monographs)
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