Thomas Scanlon, a mathematician at UC Berkeley, presents this talk at the Institute for Advanced Study's workshop on Hodge theory and o-minimality. He examines a recurring move in applications of o-minimality to unlikely intersection problems: the claim that certain analytic covering maps are definable. Scanlon shows that this claim is almost never literally true, since the maps are typically definable only on a fundamental set rather than the full domain, and that this failure of definability is itself exploited in proofs of functional transcendence. He surveys the formalisms built to handle this gap, including work by Zilber, by Bakker, Klingler, and Tsimerman, and his own earlier work with Eterović, then presents a common refinement of these approaches. The payoff is a method for deriving automatic uniformity statements from this refined framework. The talk assumes familiarity with model theory and algebraic geometry and runs through the technical machinery at research-seminar pace, aimed at specialists working at the intersection of logic and arithmetic geometry.