8 problems

Ecalle's proof concerns the injection of accelero-summable transseries into germs of functions near infinity, as used to establish the quasianalyticity needed in the analysis of po…

Let $\mathbb T$ be the differential field of logarithmic-exponential transseries, and let $\mathbb R$ be the real field. Write $\mathbb T[\imag]$ and $\mathbb C=\mathbb R[\imag]$ f…

Let $\textbf{Hy}$ be the field of hyperseries and $\textbf{No}$ the field of surreal numbers. For each hyperseries $f(x)\in\textbf{Hy}$, consider its value…

Let $\textbf{Hy}$ be the intended field of hyperseries, equipped with field operations, differentiation, and composition. Let $\Phi$ be a partial function from $\textbf{Hy}$ into i…

Let $\mathbb{T}^{\operatorname{da}}$ denote the field of accelero-summable transseries, and let $H$ be a Hardy field. In real accelero-summation, use the organic average whenever s…

Let $\mathbb{T}$ be the differential field of transseries, and let an $H$-field with small derivation be an ordered differential field satisfying the relevant $H$-field axioms and…

Consider $\mathbb{T}$ as an ordered valued differential field. The $\mathbb{T}$-conjecture. The field $\mathbb{T}$ is model complete. Equivalently, in the language of differential…

Let $\mathbb{T}$ be the ordered valued differential field of transseries. Let $H$-fields be ordered differential fields equipped with the associated $H$-field structure, and let sm…