Super-Real Fields: Totally Ordered Fields with Additional Structure (London Mathematical Society Monographs, 14) 1st Edition by H. Garth Dales (PDF)

Description

Super-fields are a class of totally ordered fields that 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 an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky’s embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.

User’s Reviews

Editorial Reviews: 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 About the Author H. Garth Dales is at University of Leeds. W. H. Woodin is at University of California, Berkeley.

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