Irredundant Sets in Atomic Boolean Algebras

TL;DR

This paper constructs an atomic Boolean algebra under GCH where the pi-weight is smaller than the size of any maximal irredundant family, challenging existing assumptions about their relationship.

Contribution

It provides a novel example of an atomic Boolean algebra with a specific discrepancy between pi-weight and maximal irredundant family size under GCH.

Findings

Existence of an atomic Boolean algebra with pi-weight less than the size of maximal irredundant families.

Demonstrates the independence of certain properties of Boolean algebras from ZFC.

Highlights the impact of GCH on the structure of atomic Boolean algebras.

Abstract

Assuming GCH, we construct an atomic boolean algebra whose pi-weight is strictly less than the least size of a maximal irredundant family.