Super-Real Fields - Totally Ordered Fields With Additional Structure

Zusatztext 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 . Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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

Product details

• Authors: H. G. Woodin Dales, H. Garth Dales, H. Garth (Proessor of Pure Mathematics Dales, H. Garth Woodin Dales, H. Garth, W. Hugh Woodin, W. Hugh (Professor of Mathematics Woodin, Woodin W. Hugh
• Publisher: Oxford University Press
• Languages: English
• Product format: Hardback
• Released: 16.05.1996
• EAN: 9780198539919
• ISBN: 978-0-19-853991-9
• No. of pages: 376
• Series: London Mathematical Society Mo; London Mathematical Society Monographs; London Mathematical Society Monographs; London Mathematical Society Mo
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Logic, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Algebra / General, Mathematical logic, Real analysis, real variables