The work  deals with questions of first-order definability in algebraic function fields. In particular, it exhibits new cases in which the field of constant functions is definable, and it investigates the phenomenon of definable transcendental elements. We fix some of its proofs and make additional observations concerning definable closure in these fields.
"A note on defining transcendentals in function fields." J. Symbolic Logic 74 (4) 1206 - 1210, December 2009. https://doi.org/10.2178/jsl/1254748687