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4. Definability


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      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?


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          Problem 4.2.

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


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              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.