(This is the tenth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the ninth lecture here. Quotes by Stevo are in dark blue; some are deep, some are funny, some are paraphrased so use your judgement. As always I appreciate any type of feedback, including reporting typos, in the comments below. I am sure that this one has a ton of typos. There are also some omissions which I will try to patch up.)
- We define the Side Condition Method.
- We force the P-Ideal Dichotomy.
- A cardinal preserving modification of the side condition is discussed.
- Semi-properness is introduced, and then used to prove a fact about projectively stationary sets.
- The Strong Reflection Principle is introduced.
- Some consequences are discussed.
- A ZFC version of diamond is stated.