7 problems

Generic-derivation GEI conjecture. The theories

Let $(k,\delta)$ be a differential field of characteristic zero with field of constants $C$. Consider a first-order differential equation over $k$, and, respectively, an autonomous…

Definability and model-companion conjecture. (1) There is an $\mathcal L_{\underline{\mathcal D}}(F)$-formula which uniformly describes this set in any…

Let $\mathfrak{L}_{j}$ denote the language of the reduct associated with the differential equation of the modular $j$-function, and let $\emph{EC}$ denote the existential-closednes…

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…