Spaces of Orderings and Abstract Real Spectra

This work should be of interest to both students and professionals 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 theory of abstract real spectra (also called spaces of signs) are included. The reader requires an elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.