(This is the fifteenth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the fourteenth 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.)

**Summary**

- We introduce free sequences.
- A lemma (2) relating free sequences and -bases is proved.
- We prove that the generic ultrafilter is countably generated.
- We construct nice -disjoint -bases.
- A realted theorem about compact spaces supporting a radon measure is proved as a corollary.