Submission date: 15 June 2012.

Abstract:

Working in an o-minimal expansion of the real field, we investigate when a germ (around 0 say) of a complex analytic function has a definable analytic continuation to its Mittag-Lffler star.
As an application we show that any algebro-logarithmic function that is complex analytic in a neighbourhood of the origin in C has an analytic continuation to all but finitely many points in C.

It is my pleasure to dedicate this paper to Anand Pillay on the occasion of his 60th birthday.

Mathematics Subject Classification:

Keywords and phrases:

Full text: pdf, dvi, ps.