Polymultisets, Multisuccessors, and Multidimensional Peano Arithmetics
Alexander Chunikhin · arXiv (Cornell University) · 2011
The goal of this paper is introduction of a concept of natural multidimensional numbers and to construct a generalized Peano arithmetic of these multidimensional numbers. For this purpose we define a polymultiset as a special set-like form of m-ary multirelation. In addition, multisuccessor and multipredecessor functions on polymultisets are determined. By introducing Peano-like axioms for natural multidimensional numbers, we build a commutative semiring of 2-numbers .