The small index property for countable superatomic boolean algebras

TL;DR

This paper proves that all countable superatomic boolean algebras of finite rank possess the small index property, advancing understanding of their automorphism groups and structural features.

Contribution

It establishes the small index property for all countable superatomic boolean algebras of finite rank, a previously unproven class.

Findings

All such algebras have the small index property.

The result applies to countable superatomic boolean algebras of finite rank.

It enhances the classification of automorphism groups in Boolean algebras.

Abstract

It is shown that all the countable superatomic boolean algebras of finite rank have the small index property.