On the First-Order Theory of Real Exponentiation

1. Auflage 2008
ISBN: 978-88-7642-325-3
Verlag: Edizioni della Normale

Buch, Englisch, Band 6, 107 Seiten, Format (B × H): 154 mm x 242 mm, Gewicht: 351 g

Reihe: Publications of the Scuola Normale Superiore

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.

Zielgruppe

Research

Autoren/Hrsg.

Servi, Tamara

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

1. Definably complete structures.- 2. Noetherian differential rings of functions.- 3. Effective o-minimality.- 4. Remarks on the decidability problem for the real exponential field.