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 of ordered 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.
- ISBN10 0198539916
- ISBN13 9780198539919
- Publish Date 16 May 1996
- Publish Status Active
- Publish Country GB
- Publisher Oxford University Press
- Imprint Clarendon Press
- Format Hardcover
- Pages 376
- Language English