Spaces of Orderings and Abstract Real Spectra

Murray A. Marshall (auth.)3540617299, 9783540617297

This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

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Table of contents :
Introduction….Pages 1-4
Orderings on fields….Pages 5-17
Spaces of orderings….Pages 19-35
Fans and the representation theorem….Pages 37-59
P-structures, connected components and 0 the isotropy theorem….Pages 61-82
The real spectrum of a ring….Pages 83-97
Abstract real spectra….Pages 99-131
Minimal generation of constructible sets….Pages 133-150
Structure results and realization results….Pages 151-181