LOGICAL THEORIES OF ONE-PLACE FUNCTIONS ON THE SET OF NATURAL NUMBERS
Aleksei L Semenov · Mathematics of the USSR-Izvestiya · 1984
In this paper the author studies the decision problem for logical languages intended to describe the properties of one-place functions on the set of natural numbers. For functions taking a finite number of values a criterion for decidability of the monadic theory of the structure is obtained. For a large class of monotone functions , conditions are found under which the elementary theory of the structure is decidable; corresponding conditions are also found for structures of the form .Bibliography: 20 titles.