On Strongly Positive Multidimensional Arithmetical Sets - Manukian, Seda N. (Mathematical Problems of Computer Science, 2021)
The notion of positive arithmetical formula in the signature (S,=,0), where S(x)=x+1, is defined and investigated in [1] and [2]. A multidimensional arithmetical set is said to be positive if it is determined by a positive formula. Some subclass of the class of positive sets, namely, the class of strongly positive sets, is considered. It is proved that for any n ≥ 3 there exists a 2n -dimensional strongly positive set such that its transitive closure is non-recursive. On the other side, it is noted that the transitive closure of any 2-dimensional strongly positive set is primitive recursive.