ENGLISH

Super-Real Fields: Totally Ordered Fields with Additional Structure

By H. Garth Dales , W. Hugh Woodin

Book information

Publisher
Oxford University Press, USA
Year
1996
ISBN
0198539916, 9780198539919
Language
english
Format
DJVU
Filesize
6 MB (6668472 bytes)
Series
London Mathematical Society Monographs
Pages
376\376
DPI
600
Time added
2014-01-22 17:29:55

Description

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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