Tag: small cardinals

Stevo’s Forcing Class Fall 2012 – Class 4

(This is the fourth lecture in Stevo Todorcevic’s Forcing class, held in the fall of 2012. You can find the third 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 look at the real reason that regular open algebras don’t collapse \omega_1 to \omega .
  • Show there is a \sigma -linked, non \sigma -centred poset of size \mathfrak{p} .
  • Introduce the cardinal \theta_2 , related to Chang’s Conjecture.
  • Introduce the idea of a functor on ccc posets.

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