The Field of Reals with Multisummable Series and the Exponential Function

2000/11/01 by Lou van den Dries, Lou Van Den Dries, Patrick Speissegger · 14 citations
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Computability, Logic, AI Algorithms

paper · doi:10.1112/s0024611500012648

Abstract

We show that the field of real numbers with multisummable real power series is model complete, o-minimal and polynomially bounded. Further expansion by the exponential function yields again a model complete and o-minimal structure which is exponentially bounded, and in which the Gamma function on the positive real line is definable. 2000 Mathematics Subject Classification: primary 03C10, 32B05, 32B20; secondary, 26E05.

Citations

• On the real exponential field with restricted analytic functions

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