Super-Real Fields: Totally Ordered Fields with Additional Structure
Hardback or Cased Book 376 pages Aug 01, 1996
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OUP Oxford
Super-Real Fields: Totally Ordered Fields with Additional Structure
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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 Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
- Author:
- H. Garth Dales
- Publisher:
- OUP Oxford
- Publication Date:
- Aug 01, 1996
- Number of pages:
- 376 pages
- Binding:
- Hardback or Cased Book
- ISBN-10:
- 0198539916
- ISBN-13:
- 9780198539919