A new minimal non-$\sigma$-scattered linear order

TL;DR

This paper demonstrates the consistency, under GCH, of a minimal non-σ-scattered linear order that contains no real or Aronszajn types, advancing the understanding of linear order structures.

Contribution

It introduces a new minimal non-σ-scattered linear order with specific properties, expanding the landscape of linear order theory.

Findings

Existence of such a linear order is consistent with GCH

The order contains no real or Aronszajn types

Provides a new example in the classification of linear orders

Abstract

We will show it is consistent with $GCH$ that there is a minimal non $\sigma$-scattered linear order which does not contain any real or Aronszajn type.