11 problems

Let $C$ be a $\partial$-independent set of cardinality $\kappa$, and let $E(C)$ be a structure prime over $C$ in the class $\mathcal{EC}$. When such a prime structure exists and is…

Let $\mathbb C_{\exp}=(\mathbb C,+,\cdot,\exp)$ be the complex exponential field, and let $\mathcal{EC}(\mathrm{ex}/\mathrm{st})$ denote the class of existentially closed structure…

Let $\Lbb$ denote the class of log-atomic surreal numbers, and let $\kappa_x$ be the kappa-number associated with a surreal number $x$ by the recursive definition … The iterated ex…

Let ${\mathbf{ELAF}}_{\lhd}$ be the category of ELA-fields with strong embeddings, where no very full kernel assumption is imposed, and let $\mathop{\mathpalette\Ind{}}^{\lhd}$ den…

Let ${\mathbb C}_{\exp}$ denote the complex field equipped with the exponential function, and assume that it satisfies the axioms of pseudo-exponentiation. Analytic Zariski conject…

Let $\mathbb{L}$ be the class of log-atomic surreal numbers, namely those $\lambda\in\mathbf{No}$ such that every iterated logarithm $\log_n(\lambda)$ is of the form $\exp(\gamma)$…

The isomorphism conjecture for the complex exponential field.

Let $(\mathbb C,+,\cdot,0,1,\exp)$ be the complex exponential field. Zilber's conjecture. The complex exponential field $(\mathbb C,+,\cdot,0,1,\exp)$ is quasi-minimal. This is a w…

Let $(V,\pi,K)$ and $(V',\pi',K')$ be structures consisting of an additive group, an exponential map, and a field, with an additional constant for a generator of the kernel of the…

Let $\mathbb{C}_{\mathrm{exp}}$ be the complex exponential field, and let $\widetilde{\mathbb{C}_{\mathrm{exp}}}$ denote its strong exponential-algebraic closure. Strong exponentia…

Four exponentials conjecture.