The FE-closure operator in countable-valued logic
Sergey Seraphimovich Marchenkov, Inna S. Kalinina · Moscow University Computational Mathematics and Cybernetics · 2013
The FE-closure operator on set P N of functions of countable-valued logic is considered. It is proved that any general recursive operator (defined in the Herbrand-Gödel formalism) can be realized in the language of FE-closure. It is established that the class of relations definable in the language of FE-closure coincides with class Σ 1 1 in the Kleene analytic hierarchy. It is shown that the membership in an FE-closed class of any nontrivial homogeneous function implies that the entire set of homogeneous functions is contained in this class.