Super-Real Fields: Totally Ordered Fields with Additional Structure
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Book Overview Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of contin...
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.
Book Details Format: Hardcover | Pages: 357 | Language: English | Publisher: OXFORD UNIV PR | ISBN: 0198539916
FormatHardcover
Pages357
LanguageEnglish
ISBN0198539916
EAN9780198539919
PublisherOXFORD UNIV PR
Publication Date1970-01-01
Edition1
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.56 Pounds
Length9.5 Inches
Width6.38 Inches
Height0.97 Inches
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