van den Dries, Lou; Speissegger, Patrick The field of reals with multisummable series and the exponential function. (English) Zbl 1062.03029 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. Cited in 4 ReviewsCited in 39 Documents 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 PDF BibTeX XML Cite \textit{L. van den Dries} and \textit{P. Speissegger}, Proc. Lond. Math. Soc. (3) 81, No. 3, 513--565 (2000; Zbl 1062.03029) Full Text: DOI