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Super-Real Fields: Totally Ordered Fields with Additional Structure (London Mathematical Society Monographs) - Hardcover
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.
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About the Author
H. Garth Dales is at University of Leeds. W. H. Woodin is at University of California, Berkeley.
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 this title" may belong to another edition of this title.
- PublisherClarendon Press
- Publication date1996
- ISBN 10 0198539916
- ISBN 13 9780198539919
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages376
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Super-Real Fields : Totally Ordered Fields With Additional Structure
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Super-Real Fields: Totally Ordered Fields with Additional Structure (London Mathematical Society Monographs)
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Super-Real Fields (Hardcover)
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Oxford University Press, Oxford, 1996
ISBN 10: 0198539916
ISBN 13: 9780198539919
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Hardcover. Condition: new. Hardcover. 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 ofordered 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. This advanced text expounds the established theory of ordered fields, and continues to develop a quite original theory of super-real fields. This theory has important applications in analysis and logic. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780198539919
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Super-Real Fields : Totally Ordered Fields With Additional Structure
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Super-Real Fields : Totally Ordered Fields With Additional Structure
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Super-real fields : totally ordered fields with additional structure / H. Garth Dales and W. Hugh Woodin
Published by
Oxford New York : Clarendon Press ; Oxford University Press, 1996
ISBN 10: 0198539916
ISBN 13: 9780198539919
Used
Hardcover
First Edition
Seller: MW Books, New York, NY, U.S.A.
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1st edition. Fine copy in the original gilt-blocked cloth. Slightest suggestion only of dust-dulling to the panel edges. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 357 pp.: illustrations ; 24 cm. Contents; 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 [actual symbol not reproducible] -- 7. Examples -- 8. Non-standard structures for super-real fields and the gap theorem -- 9. [actual symbol not reproducible] as a hyper-real field -- 10. Models and weak Cauchy completeness -- 11. Rigid fields and solid structures -- 12. Open questions. Subjects; Ordered fields. Algebraic topology. Mathematics. 1 Kg. Seller Inventory # 396998
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Super-Real Fields : Totally Ordered Fields With Additional Structure
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Super-Real Fields : Totally Ordered Fields with Additional Structure
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Buch. Condition: Neu. Neuware - 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. Seller Inventory # 9780198539919
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Super-real fields : totally ordered fields with additional structure / H. Garth Dales and W. Hugh Woodin
Published by
Oxford New York : Clarendon Press ; Oxford University Press, 1996
ISBN 10: 0198539916
ISBN 13: 9780198539919
Used
Hardcover
First Edition
Seller: MW Books Ltd., Galway, Ireland
Seller rating 5 out of 5 stars
1st edition. Fine copy in the original gilt-blocked cloth. Slightest suggestion only of dust-dulling to the panel edges. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 357 pp.: illustrations ; 24 cm. Contents; 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 [actual symbol not reproducible] -- 7. Examples -- 8. Non-standard structures for super-real fields and the gap theorem -- 9. [actual symbol not reproducible] as a hyper-real field -- 10. Models and weak Cauchy completeness -- 11. Rigid fields and solid structures -- 12. Open questions. Subjects; Ordered fields. Algebraic topology. Mathematics. 1 Kg. Seller Inventory # 396998
Quantity: 1 available
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Super-Real Fields: Totally Ordered Fields with Additional Structure: 14 (London Mathematical Society Monographs)
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HRD. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L1-9780198539919
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