(This is the seventh lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the sixth 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**

- Talk about the CH “hierarchy”.
- Point out the MA analogue.

- Show that it is possible to force a function to be continuous on a large set.
- Show that Chang’s Conjecture is preserved by ccc forcing.