Ordered Exponential Fields

Model theoretic algebra has witnessed remarkable progress in the 1990s. 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 an increasingly interesting topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a ... Read More

Model theoretic algebra has witnessed remarkable progress in the 1990s. 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 an increasingly interesting topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Read Less