Geodesic
On complexity of solving systems of functional equations in countable-valued logic
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 2, pp. 49-62

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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.
Keywords: system of functional equations, function of countable-valued logic. 
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S. S. Marchenkov. On complexity of solving systems of functional equations in countable-valued logic. Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 2, pp. 49-62. http://geodesic.mathdoc.fr/item/DA_2015_22_2_a3/