Understanding Preservation Theorems, II

TL;DR

This paper provides an exposition of key preservation theorems in forcing, focusing on properties like non-meager reals, dense open sets, and bounding, to deepen understanding of forcing techniques.

Contribution

It offers a detailed explanation of preservation theorems related to forcing, expanding on sections from a foundational text to clarify complex concepts.

Findings

Preservation of non-meager reals over V

Dense open sets contain dense open sets in V

Weak bounding and weak ω^ω-bounding properties

Abstract

This is an exposition of much of Sections VI.3 and XVIII.3 of "Proper and Improper Forcing", including preservations for "no random reals over V", "reals of V form a non-meager set", "every dense open set contains a dense open set in V", weak bounding, and weak $\omega^\omega$-bounding. The current version of part I covering Sections VI.1 and VI.2 is available from the author.