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Super-Real Fields Totally Ordered Fields with Additional Structure

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ISBN-10: 0198539916

ISBN-13: 9780198539919

Edition: 1996

Authors: H. Garth Dales, W. Hugh Woodin

List price: $100.00
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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…    
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Book details

List price: $100.00
Copyright year: 1996
Publisher: Oxford University Press, Incorporated
Publication date: 8/1/1996
Binding: Hardcover
Pages: 376
Size: 6.14" wide x 9.21" long x 0.87" tall
Weight: 1.496

Dr W. Hugh Woodin is a Professor of Mathematics and the Chair of the Mathematics Department at the University of California, Berkeley. Professor Woodin has published numerous articles and books and is the managing editor of the Journal of Mathematical Logic and editor of Mathematical Research Letters, Mathematical Logic Quarterly and Electronic Research Announcements (American Mathematical Society).

Introduction
Ordered sets and ordered groups
Ordered fields
Completions of ordered groups and fields
Algebras of continuous functions
Normability and universality
The operational calculus and the field R
Examples
Non-standard structures for super-real fields and the gap theorem
R as a hyper-real field
Models and weak Cauchy completeness
Rigid fields and solids structures
Open questions