Composition of infinitary structures

G. G. Ryabov, V. A. Serov

Lomonosov Moscow State University, Research Computing Center

Abstract: The infinitary structure of an $n$-cube, global $k$-ary trees, and natural numbers are considered as a single genetic structure. A number of geometric characteristics of the shortest paths in an $n$-cube are specified and the properties of prime number symmetry among the natural numbers are studied on the basis of this structure.

Keywords: $n$-куб, $n$-cube, symbolic matrix, global $k$-ary tree, $k$-tuples of natural numbers, difference tabloid, symmetry of prime numbers, incompatibility relatio.

UDC: 512.531; 515.124; 004.2

Received: 10.09.2015