More on almost Souslin Kurepa trees

TL;DR

This paper demonstrates the consistency of a Souslin tree transforming into an almost Souslin Kurepa tree after forcing, addressing a question posed by Zakrzewski.

Contribution

It provides a consistency result showing the existence of a Souslin tree that becomes an almost Souslin Kurepa tree through forcing, answering an open question.

Findings

Existence of a Souslin tree that becomes an almost Souslin Kurepa tree after forcing

Addresses a question of Zakrzewski about tree transformations

Shows consistency results in set theory regarding tree properties

Abstract

It is consistent that there exists a Souslin tree $T$ such that after forcing with it, $T$ becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski.