(These are the

~~voyages are the starship enterprise~~notes from Arnie Miller’s guest lecture in Alan Dow’s Forcing course, held on October 11, 2012. The lecture was a self-contained exploration of~~strange new worlds~~Namba forcing. (Alright, I will stop doing that. For those who don’t get the reference.) Arnie Miller’s quotes are in Grey. Yes, the forcing checks are ugly. I have yet to figure that one out.)

**Summary**

- Motivation with posets that collapse cardinals.
- Namba Trees are defined.
- Two 0-extension lemmas are proved.
- The Fat Namba Filter is introduced.
- An important theorem of Namba’s is proved.