Almost Souslin Kurepa trees

TL;DR

This paper demonstrates the consistency of almost Souslin Kurepa trees within ZFC and proves their existence in the constructible universe L, addressing open questions in set theory.

Contribution

It establishes the consistency and existence of almost Souslin Kurepa trees in ZFC and L, resolving two questions posed by Zakrzewski.

Findings

Almost Souslin Kurepa trees are consistent with ZFC.

Such trees exist in the constructible universe L.

Answers two open questions in set theory.

Abstract

We show that the existence of an almost Souslin Kurepa tree is consistent with $ZFC$. We also prove their existence in $L$. These results answer two questions from Zakrzewski.