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4. Definability


    1. Add remark

      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?


        • Add remark

          Problem 4.2.

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


            • Add remark

              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.