Shelah's strong covering property and CH in V[r]

TL;DR

This paper reviews Shelah's strong covering property, explores its applications, and extends results on the failure of the continuum hypothesis by adding a real, contributing to set theory and forcing techniques.

Contribution

It introduces new extensions of Shelah and Woodin's results on CH failure through real addition, enhancing understanding of covering properties.

Findings

Shelah's strong covering property is applicable in set theory.

Adding a real can cause the failure of CH under certain conditions.

Extensions of Shelah and Woodin's results are established.

Abstract

In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $CH$ by adding a real.