The field of reals with multisummable series and the exponential function. (English) Zbl 1062.03029

van den Dries, Lou; Speissegger, Patrick

Proc. Lond. Math. Soc., III. Ser. 81, No. 3, 513-565 (2000).

Summary: 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.

MSC:

03C64	Model theory of ordered structures; o-minimality
03C10	Quantifier elimination, model completeness and related topics
12L12	Model theory of fields
26E05	Real-analytic functions

Keywords:

field of real numbers with multisummable real power series; exponential function; o-minimal structure; Gamma function on the positive real line; model completeness; blowing-up