<p>Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed fields, the structure of the non-archimedean models in the semi-algebraic case is well understood. For the o-minimal case, so far there has been no systematic study of the non-archimedean models. The goal of this monograph is to serve this purpose. The author presents a detailed description of the non-archimedean models of the elementary theory of certain o-minimal expansions of the reals in which the exponential function is definable. The example of exponential Hardy fields is worked out with particular emphasis. The basic tool is valuation theory, and a sufficient amount of background material on orderings and valuations is presented for the convenience of the reader.</p>

Ordered Exponential Fields (Fields Institute Monographs, 12)

Science & Math

Salma Kuhlmann

Mathematics

American Mathematical Society, Fields Institute

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Books by Salma Kuhlmann

See the best price to sell, buy, or rent books by Salma Kuhlmann. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Ordered Exponential Fields (Fields Institute Monographs, 12)