For my honours thesis, I am studying a general preservation theorem using a framework provided by Shelah. I am mainly concerned about revised countable support iteration of $\dot{S}$-semiproper forcing notions, for a specific class of $\dot{S}$. For the introduction to my paper, I wish to include a historical background of the study of preservation theorems.
A preservation theorem is generally a statement of the form: "If $\bar{Q}$ is an X iteration with all iterands (here it depends on how you define an iterand) having property $P$, then $lim(\bar{Q})$ has property $P$." In this case, we say property $P$ is preserved under $X$ iteration.
I know one of the landmarks is Shelah's prove of the preservation of $``^{\omega}{\omega}$-bounding + properness$"$ under CS iteration. Also, there are a number of preservation theorems under various iterations investigated by Shelah in the 1980s-1990s, most of which can be found in his book Proper and Improper Forcing. But what are the works leading up to Shelah's contributions? I hope to put together a chronology of the important preservation theorems.
Thanks in advance.
