TY - JOUR
AU - Manukian, Seda N.
PY - 2021/12/10
Y2 - 2024/05/18
TI - On Strongly Positive Multidimensional Arithmetical Sets
JF - Mathematical Problems of Computer Science
JA - MPCS
VL - 43
IS -
SE - Articles
DO -
UR - http://mpcs.sci.am/index.php/mpcs/article/view/205
SP - 32-41
AB - <p>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.</p>
ER -