Action of an FE-Closure operator on functions of countable-valued logic
Inna S. Kalinina · Moscow University Computational Mathematics and Cybernetics · 2014
An FE-closure operator based on systems of functional equations is considered for a set of functions of countable-valued logic. It is proved that the FE-closure of sets similar to {0, x + 1} coincides with class Σ 1 1 in the Kleene analytic hierarchy. The FE-closure of systems with characteristic functions for congruence relations is studied. It is shown that the family of FE-closed classes has the cardinality of the hypercontinuum.