Multisummability for generalized power series
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abstract

We develop multisummability, in the positive real direction, for generalized
power series with natural support, and we prove o-minimality of the expansion
of the real field by all multisums of these series. This resulting structure
expands both $\mathbb{R}_{\mathcal{G}}$ and the reduct of
$\mathbb{R}_{\mathrm{an}^*}$ generated by all convergent generalized power
series with natural support; in particular, its expansion by the exponential
function defines both the Gamma function on $(0,\infty)$ and the Zeta function
on $(1,\infty)$.