Abstract: 

Transseries emerged in connection with Écalle’s work on Dulac’s problem and Dahn and Göring’s work on nonstandard models of real exponentiation, and some can be viewed as asymptotic expansions of solutions to differential equations. More recently, Aschenbrenner, Van den Dries, and Van der Hoeven completely axiomatized the elementary theory of the differential field of (logarithmic-exponential) transseries and showed that it is model complete. This talk concerns pairs of models of this theory such that one is a tame substructure of the other in a certain sense. I will describe the model theory of such transserial tame pairs, including a model completeness result for them, which can be viewed as a strengthening of the model completeness of large elementary extensions of the differential field of transseries, such as hyperseries, surreal numbers, or maximal Hardy fields.

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