For an approach based on language in the calculus of first-order predicates with equality and negation, which has numerical semantics and is used to create executable logical prototypes for modeling complex systems, the possibility of extending specifications with built-in arithmetic is being investigated. Sufficient conditions for the finite completeness of the interpretation of definitions for specifications extended by built-in, externally interpreted arithmetic, the use of which increases the expressiveness of descriptions, have been determined. The conditions are checked syntactically, according to the type of theory, for a time not exceeding O(n2) the relative symbolic length of the chain encoding the theory. The applicability of the extended approach for modeling dynamic systems is shown.