Title: Super-Real Fields: Totally Ordered Fields with Additional Structure (London Mathematical Society Monographs)
Publisher: Clarendon Press
Publication Date: 1996
Language: English
ISBN 10: 0198539916
ISBN 13: 9780198539919
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

About the Author

H. Garth Dales is at University of Leeds. W. H. Woodin is at University of California, Berkeley.

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