
## 4. Definability

1. #### Problem 4.1.

1. Is $\mathbb C[t_1,\dots, t_n]$ definable in $\mathbb C(t_1,\dots, t_n)$?
2. Is there a diophantine definition?
• #### Problem 4.2.

Define a non-trivial valuation on $\mathbb C(t_1,\dots, t_n)$.
• #### Problem 4.3.

Is $(\mathbb Z, +, \cdot)$ definable as a subring by first-order formulas in $\mathbb C(t_1,\dots, t_k)$?

Cite this as: AimPL: Definability and decidability problems in number theory, available at http://aimpl.org/definedecide.