Chain homogeneous Souslin algebras

TL;DR

This paper constructs special Souslin algebras under certain set-theoretic assumptions, where all maximal chains are isomorphic, addressing longstanding questions in the structure of such algebras.

Contribution

It introduces a method to build Souslin algebras with all maximal chains pairwise isomorphic, advancing understanding of their order-theoretic properties.

Findings

All maximal chains in the constructed algebras are pairwise isomorphic.

The construction relies on Jensen's diamond-plus principle.

Answers specific open questions by Koppelberg and Todorcevic.

Abstract

Assuming Jensen's principle diamond-plus we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todorcevic