Abstract
In this chapter we shall give Artin’s solution (2.1.12) to Hilbert’s 17th problem as explained in the Introduction. The “specialization” arguments developed by Artin will be incorporated in Tarski’s Transfer Principle (2.1.10). In order to prove the latter, we briefly introduce ultraproducts, and use some arguments that originated in Model Theory. In the last section of this chapter we prove the so-called “Finiteness” Theorem, which will be used in Chapter 4 to obtain an improved solution of Hilbert’s 17th problem.
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© 2001 Springer-Verlag Berlin Heidelberg
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Prestel, A., Delzell, C.N. (2001). Semialgebraic Sets. In: Positive Polynomials. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04648-7_3
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DOI: https://doi.org/10.1007/978-3-662-04648-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07445-5
Online ISBN: 978-3-662-04648-7
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