Definability in the language of functional equations of a countable-valued logic
Sergey Seraphimovich Marchenkov · Discrete Mathematics and Applications · 2013
The paper is concerned with definability of functions and relations in the FE language of functional equations of a countable-valued logic. The class of relations definable by functional equations over the set of functions {0, x + 1} is shown to coincide with the class ∑ 1 1 of the analytical Kleene hierarchy. Two extensions of the FE language are proposed that are equivalent in their expressibility to the FE language with functional constants for all homogeneous functions. This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 13-01-00958).