Introducing a nontrivial square_omega

TL;DR

This paper introduces a nontrivial version of the square principle 1_5, demonstrates its consistency via finite condition forcing, but is withdrawn because the principle can be constructed in ZFC.

Contribution

It presents a nontrivial 1_5 construction and forcing method, later shown to be unnecessary as the principle is provable in ZFC.

Findings

The 1_5 can be constructed in ZFC.

Forcing with finite conditions was used to show consistency.

The initial claim of a nontrivial 1_5 was withdrawn.

Abstract

We define a nontrivial version of the square principle $\Box_\omega$, which we then show consistent by means of forcing with finite conditions. This paper has been withdrawn by the author due to the fact that the presented $\Box_\omega$ can be constructed in ZFC, as shown by Lajos Soukup and Philip Welch. Note, that the forcing itself has not been found flawed.