On the First-Order Theory of Real Exponentiation
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Beschreibung
The first-order theory of real exponentiation has been studied by many mathematicians in the last fifty years, in particular by model theorists, real geometers and number theorists. The aim of this work is to present the results obtained so far in this area and to improve and refine them. In the early 1990s A. Macintyre and A.J. Wilkie proved that the theory of real exponentiation is decidable, provided that Schanuel’s conjecture holds. In the proof of their result, they proposed a candidate for a complete and recursive axiomatization of the theory. While simplifying their axiomatization, the author of this book analyses (in the first three chapters) the model theory and geometry of a broad class of functions over real closed fields. Even though the methods used are elementary, the results hold in great generality. The last chapter is devoted solely to the decidability problem for the real exponential field.
Provides both new scientific content and an overview of the research done so far on this subject
First book on this subject written for a broader audience; published research articles are very technical
Autor*in
Tamara Servi
Themen in »On the First-Order Theory of Real Exponentiation«
algebraic geometry model theory o-minimal geometry quasi-analytic geometry real analytic geometry transcentental number theory