| Résume | This talk discusses the model theory of expansions of the real field by families of functions from quasianalytic classes, with a model completeness construction of Rolin, Speissegger, and Wilkie (J. Am. Math. Soc., vol. 16, no. 4, 2003) playing a central role. This construction is comprised of three ingredients: (1) local desingularization, (2) fiber cutting, and (3) a general theorem of the complement based on the ``Gabrielov property''. Without getting into much technical detail of these three ingredients, part of my aim in this talk is to explain the utility of replacing the noninvariant (local) desingularization procedure in the original proof with an invariant (global) desingularization procedure that keeps track of parameters in a natural way and to develop some of the basic properties of these quasianalytic classes upon which such a desingularization procedure is based. |
