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1. Computability


    1. Add remark

      Problem 1.1.

      [Russell Miller] Given f\in \mathbb Z[x_1,\dots, x_n], define the following sets. A(f) = \{\text{subrings of }\mathbb Q \text{ where $f$ has a solution}\}
      \mathcal C(f) = \text{The interior of the complement of $A(f)$}
      B(f) =\text{The boundary of the complement of $A(f)$} %= \text{``the boundary set"}
      1. Can the Lebesgue measure of B(f) be positive?
      2. If so, what is the maximal complexity of the measure of B(f)?
      3. Is \mathcal C(f) always a finite union of basic open sets?

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