Sacks Forcing and the Shrink Wrapping Property

TL;DR

This paper introduces the shrink wrapping property, a stronger condition than the Sacks property, analyzes its behavior under different forcing extensions, and demonstrates its application in set theory.

Contribution

It defines the shrink wrapping property, compares it with the Sacks property, and explores its presence in Sacks and Silver forcing extensions.

Findings

Shrink wrapping property is stronger than the Sacks property.

It holds in Sacks forcing extensions but not in Silver forcing extensions.

Application of the property demonstrates its usefulness in set theory.

Abstract

We consider a property stronger than the Sacks property, called the shrink wrapping property, which holds between the ground model and each Sacks forcing extension. Unlike the Sacks property, the shrink wrapping property does not hold between the ground model and a Silver forcing extension. We also show an application of the shrink wrapping property.