A note on asymptotic density

TL;DR

This paper proves that the quotient of the power set of natural numbers by the ideal of density-zero sets is a universal structure for embeddings, highlighting its foundational role in asymptotic density theory.

Contribution

It establishes the universality of the quotient structure of sets modulo asymptotic density zero, a novel insight in the study of asymptotic density.

Findings

The quotient structure is universal for embeddings.

The ideal of density-zero sets is well-characterized.

Provides a new perspective on asymptotic density in set theory.

Abstract

It is proved that $P(\omega)/\triangle_d$, where $\triangle_d$ is the ideal of sets of asymptotic density zero, is universal in the sense of embeddings.