Working in an o-minimal expansion of the real field, we investigate when a germ (around zero, say) of a complex analytic function has a definable analytic continuation to its Mittag–Leffler star.
As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in has an analytic continuation to all but finitely many points in .
"Some Results and Problems on Complex Germs with Definable Mittag–Leffler Stars." Notre Dame J. Formal Logic 54 (3-4) 603 - 610, 2013. https://doi.org/10.1215/00294527-2143979