# On Strongly Positive Multidimensional Arithmetical Sets

## Keywords:

Arithmetical formula, Transitive closure, Recursive set, Signature## Abstract

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.

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*Mathematical Problems of Computer Science*,

*43*, 32–41. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/205

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