A minimal Kurepa tree with respect to club embeddings

TL;DR

This paper demonstrates the consistency of the existence of a minimal Kurepa tree with respect to club embeddings under the Generalized Continuum Hypothesis, contributing to set theory and tree combinatorics.

Contribution

It introduces the concept of a minimal Kurepa tree with respect to club embeddings and proves its consistency with GCH, a novel result in the field.

Findings

Existence of a minimal Kurepa tree with respect to club embeddings is consistent with GCH.

Provides a new construction or proof technique for such trees.

Advances understanding of Kurepa trees and their embeddings.

Abstract

We will show it is consistent with $GCH$ that there is a minimal Kurepa tree with respect to club embeddings.