Independence of higher Kurepa hypotheses

TL;DR

This paper investigates the independence of higher Kurepa hypotheses, demonstrating that certain hypotheses do not imply others under specific large cardinal assumptions, highlighting their independence.

Contribution

It proves that the Gap-$n$-Kurepa hypothesis is independent of the Gap-$m$-Kurepa hypothesis for different n and m, assuming an inaccessible cardinal.

Findings

Gap-$n$-Kurepa hypothesis does not follow from Gap-$m$-Kurepa hypothesis for m ≠ n

Inaccessible cardinals are necessary for these independence results

The results clarify the relationships among higher Kurepa hypotheses

Abstract

We study the Generalized Kurepa Hypothesis introduced by Chang. We show that relative to the existence of an inaccessible cardinal the Gap-$n$-Kurepa hypothesis does not follow from the Gap-$m$-Kurepa hypothesis for $m$ different from $n$. The use of an inaccessible is necessary for this result.