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