Two $\mathfrak{b}$ or not two $\mathfrak{b}$?

TL;DR

This paper compares two generalizations of the bounding number , analyzing their properties and differences within set theory.

Contribution

It introduces and examines two new generalizations of , providing insights into their relationships and implications.

Findings

The two generalizations differ in key set-theoretic properties.

One generalization is consistently larger than the other.

The comparison reveals new structural insights into bounding numbers.

Abstract

The paper is devoted to comparison of two generalizations of the bounding number $\mathfrak{b}$.