Tag: Functor

Stevo’s Forcing Class Fall 2012 – Class 6

(This is the sixth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the fifth 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 talk about some caliber properties.
  • Establish that the ccc functor really goes to ccc spaces.
  • Use this to create an interesting ccc poset.
  • Talk about some combinatorial versions of CH.
  • Mention a few consequences of CH^3 .

Continue reading Stevo’s Forcing Class Fall 2012 – Class 6

Stevo’s Forcing Class Fall 2012 – Class 5

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

Sumary

  • Mention something about Cohen and Random Forcing.
  • We recall some facts about \theta_2 .
  • Establish some lemmas about \theta_2 .
  • Give most of the proof of the functor on ccc posets.

Continue reading Stevo’s Forcing Class Fall 2012 – Class 5