On the First-Order Theory of Real Exponentiation Zoom

Tamara Servi

On the First-Order Theory of Real Exponentiation

pp. xii-110

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Product Description


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.

Additional Information

Additional Information

Title On the First-Order Theory of Real Exponentiation
Author (display) Tamara Servi
Editing/translations No
ISBN 978-88-7642-325-3
Publishing year 2008
Subject Matematica e storia della matematica
Buy link http://www.springer.com/birkhauser/mathematics/scuola+normale+superiore/book/978-88-7642-325-3
Notes No