On complexity of solving systems of functional equations in countable-valued logic

We propose a procedure to construct all solutions of an arbitrary system of functional equations in countable-valued logic. Based on this procedure, the solutions of systems of equations in the class $\Sigma_2$ of Kleene–Mostovsky arithmetical hierarchy which include only the ternary discriminator $p$ are determined. We prove that for given systems of equations the components of solutions may be arbitrary functions of the class $\Sigma^1_1$ of Kleene analytical hierarchy. Bibliogr. 10.