Helmut Wolter

ON THE THEORY OF EXPONENTIAL FIELDS

In the present paper we investigate different classes of exponential fields with the intention to get more information on such classes of structures and their theories in order to give perhaps a contribution to the solution of the decidability problem of (R, e ) where R is the field of real numbers and e the usual exponential function on R. This problem goes back to A. TARSRI and has been treated recently by several people

On roots of exponential terms

In the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms (with one variable). The result were obtained by generalizing Sturms technique for real closed fields. Moreover for arbitrary non-zero terms t(x) certain estimations concerning the location of roots of t(x) are given. MSC: 03C65, 03C60, 12L12.

Consequences of Schanuel's condition for zeros of exponential terms

Assuming “Schanuels Condition” for a certain class of exponential fields, Sturms technique for polynomials in real closed fields can be extended to more complicated exponential terms in the corresponding exponential field. Hence for this class of terms the exact number of zeros can be calculated. These results give deeper insights into the model theory of exponential fields. MSC: 03C65, 03C60, 12L12.