On Weak Projectivity in Arithmetic

Authors

  • Mark Burgin UCLA

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3545

Keywords:

Arithmetic, Prearithmetic, Vector expansion, Matrix expansion, Addition, Multiplication, Projectivity, Category

Abstract

In the 19th century, non-Euclidean geometries were discovered and studied. In the 20th century, non-Diophantine arithmetics were discovered and studied. Construction of non-Diophantine arithmetics is based on very general mathematical structures, which are called abstract prearithmetics, as well as on the projectivity relation between abstract prearithmetics. In a similar way, as set theory gives a foundation for mathematics, the theory of abstract prearithmetics provides foundations for the theory of the Diophantine and non-Diophantine arithmetics. In this paper, we study relations between operations in abstract prearithmetics exploring how properties of operations in one prearithmetic impact properties of operations in another prearithmetic. In addition, we explore how to build new prearithmetics from existing ones.

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Published

2019-11-01

Issue

Section

Nonlinear Analysis

How to Cite

On Weak Projectivity in Arithmetic. (2019). European Journal of Pure and Applied Mathematics, 12(4), 1787-1810. https://doi.org/10.29020/nybg.ejpam.v12i4.3545