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On the First-Order Theory of Real Exponentiation

Tamara Servi (Autor)

Buch | Softcover

107 Seiten

2008
Scuola Normale Superiore (Verlag)
978-88-7642-325-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.3.2008
Reihe/Serie	Publications of the Scuola Normale Superiore ; 6
Reihe/Serie	Theses (Scuola Normale Superiore)
Zusatzinfo	XIV, 107 p.
Verlagsort	Pisa
Sprache	englisch
Maße	150 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	88-7642-325-7 / 8876423257
ISBN-13	978-88-7642-325-3 / 9788876423253
Zustand	Neuware